Convert the following amounts into the units required, correct to 2 decimal places where necessary:
2500 metres into kilometres
2100 seconds into minutes
7.562 kilometres into metres
6.85 hours into seconds
For each of the following pairs of speeds, state which one is faster and explain your answer:
60 \text{ m/h} and 60 \text{ km/h}
70 \text{ m/h} and 70 \text{ m/s}
Convert the following speeds:
14 \text{ m/s} into \text{km/h}
45 \text{ km/h} into \text{m/s}
Calculate the average speed of the following journeys:
Maria travels by car for 420 \text{ km} which takes 10 hours.
A bus leaves the depot at 6:00 am and 324.5 \text{ km} later arrives at 11:30 am.
At 11:45 am, Christa and Sharon leave to drive 96 \text{ km} from Sydney to Brisbane. They arrive at 1:15 pm.
Sally states that her trip between Brisbane and Townsville had an average speed of 91 \text{ km/h}. The table shown displays the distances between two towns (in kilometres).
How long did it take Sally to travel from Brisbane to Townsville? Give your answer correct to two decimal places.
| To Cairns | To Darwin | To Melbourne | To Perth | To Sydney | To Townsville | |
|---|---|---|---|---|---|---|
| From Brisbane | 1717 | 3415 | 1674 | 4384 | 996 | 1467 |
| From Cairns | 0 | 2727 | 3054 | 5954 | 2546 | 374 |
| From Darwin | 2727 | 0 | 3781 | 4045 | 4000 | 2556 |
| From Melbourne | 3054 | 3781 | 0 | 3452 | 868 | 2857 |
| From Perth | 5954 | 4045 | 3452 | 0 | 4144 | 5728 |
| From Sydney | 2546 | 4000 | 868 | 4144 | 0 | 2494 |
| From Townsville | 374 | 2556 | 2857 | 5728 | 2494 | 0 |
The table below shows the distances between various locations in Australia in kilometres:
| Brisbane | Sydney | Canberra | Melbourne | Adelaide | Perth | |
|---|---|---|---|---|---|---|
| Brisbane | 0 | 1010 | 1268 | 1669 | 3100 | 4384 |
| Sydney | 1010 | 0 | 288 | 963 | 1427 | 4110 |
| Canberra | 1268 | 288 | 0 | 647 | 1204 | 3911 |
| Melbourne | 1669 | 963 | 647 | 0 | 728 | 3430 |
| Adelaide | 3100 | 1427 | 1204 | 728 | 0 | 2725 |
| Perth | 4384 | 4110 | 3911 | 3430 | 2725 | 0 |
Derek wants to travel from Adelaide to Perth. Answer the following, rounding all answers to two decimal places:
How long would it take him to make the trip by bus, if it travels at an average speed of 78 \text{ km/h}?
How long would it take him to make the trip by train, if it travels at an average speed of 237 \text{ km/h}?
How long would it take him to make the trip by car, if it travels at an average speed of 96 \text{ km/h}?
If the average speed of a journey was 63 \text{ km/h}, state whether each of the following statements are true or false:
The minimum speed of the journey was 63 \text{ km/h}.
The maximum speed over the journey was 63 \text{ km/h}.
63 \text{ km} was travelled in exactly 1 hour.
The speed could have waivered above and below the speed of 63 \text{ km/h}.
The journey took 1 hour.
Sally tells Neil that her trip from Uppity to Downtown had an average speed of 90 \text{ km/h}. State whether each of the following statements are true or false:
The trip covered a distance of 1080 \text{ km} over 12 hours.
The trip covered a distance of 3 \text{ km} over 270 hours.
The trip covered a distance of 1080 \text{ km} over 3 hours.
The trip covered a distance of 270 \text{ km} over 3 hours.
Find the distance travelled in kilometres, if a car travels at:
85 \text{ km/h} for 5.4 hours.
30 \text{ m/s } for 19 minutes. Round your answer to one decimal place.
Find the speed of a vehicle in kilometres per hour if it travelled:
150 kilometres over 5 hours.
360 metres over 45 seconds. Round your answer to one decimal place.
Find how long the following journeys took, in minutes, if a car travelled at:
29 \text{ km/h} and covered 139.2 \text{ km}
32 \text{ m/s }and covered 24\text{ km}
A man drives a truck 144 \text{ km} in 2 hours, then stops to refuel and eat lunch at a petrol station for an hour. He then drives the truck for another 5 hours, covering 96 \text{ km}.
What was the truck’s average speed throughout the whole journey (in kilometres per hour)?
A woman runs 2.4 \text{ km} at a speed of 8 \text{ m/s}, then rests for 15 minutes. She then drives to the gym 15 \text{ km }away at a speed of 75 \text{ km/h}.
Calculate the time she takes to complete her run (excluding rest time).
Find the time it takes for her to drive to the gym.
What is the total time of the journey?
A round car trip averages 120 \text{ km/h} on a motorway for 1.5 hours, then averages 45 \text{ km/h} on suburban streets for 2 hours and averages 30 \text{ km/h} for 1.5 hours in school zones.
What is the total distance the car has travelled?
Christa made a trip to her friend's house and back. The trip there took 2.7 hours and the trip back took 2.9 hours. She averaged a speed of 80 \text{ km/h} over the entire return trip there and back.
How many kilometres in total did Christa travel in the going and return trip?
If the trip from her friend's house to home was 215.04 \text{ km} long, how far was the trip going from home to her friend's house?
Valentina is going to a BBQ on an island in the harbour. She has the option to take a jetski, where the journey is 194 \text{ km} directly across the water, or take the bus where the journey will be 130.5 \text{ km} around the harbour and across on the ferry.
Using the speeds supplied in the table, determine which method of transport provides the quickest way to get there.
| Transportation | Jetski | Bus |
|---|---|---|
| \text{Speed (km/h)} | 119 | 65 |
James and Valentina left the airport at the same time and immediately started travelling in opposite directions on the freeway, with James travelling at 42 \text{ km/h} and Valentina travelling at 33 \text{ km/h}. How far apart were they after 2.2 hours?
Katrina and Ned both left the office and started travelling directly toward the store, but Ned left 3 hours after Katrina, traveling at 88 \text{ km/h}. Four hours after Ned had left the office, both of them arrived at the store at the same time.
How many kilometres did Ned travel to reach the store?
What was Katrina's average speed throughout her journey? Round your answer to one decimal place.
Carl and Amelia left different places at the same time and are travelling in the same direction. Carl travelled at an average speed of 21 \text{ km/h}. Amelia travelled at an average speed of 64 \text{ km/h}.
If Carl travelled 231 \text{ km} before Amelia caught up with him, find t, the time in hours that it took Amelia to catch up with Carl.
Find the additional distance that Amelia had to travel compared to Carl.
If a car's braking distance is 25 metres and the driver's reaction time distance is 27 metres, what is the total stopping distance?
If a driver’s reaction time is 2.2 seconds and his vehicle is travelling at 50\text{ km/h}, what is the reaction time distance in metres? Round your answer to two decimal places.
A driver’s reaction time is 2.4 seconds. How far will a car travel in those 2.4 seconds if it is moving at the following speed before the brakes are applied:
30 \text{ km/h}
90 \text{ km/h}
Gemma is driving at 100 \text{ km/h} when she has to brake suddenly and bring her car to a complete stop. Her reaction time is 2.9 seconds and the braking distance is 103 metres.
Calculate her stopping distance in metres. Round your answer to one decimal place.
The braking distance for a car moving at 90 \text{ km/h} on a dry road is 83 metres. If the road is wet, the braking distance increases to 103 metres.
How much extra distance, in metres, does the car need for braking on a wet road when travelling at 90 \text{ km/h}?
If the car is 4.5 metres long, how many car lengths is this extra distance. Round your answer to one decimal place.
Sophia drives her car at 80 \text{ km/h} on the freeway. Her car's braking distance is 36 metres on a dry road and 52 metres when the road is wet. Her reaction time is 2.3 seconds in both cases.
Calculate her stopping distance in metres if the road is dry. Round your answer to one decimal place.
Calculate her stopping distance in metres if the road is wet. Round your answer to one decimal place.
Two cars are travelling side by side on adjacent lanes of a freeway. Both cars are moving at the same speed of 110 \text{ km/h}. They see a hazard on the road ahead at the same time, and apply their brakes to bring their cars to a complete stop.
Derek's car has a braking distance of 74 metres and Derek's reaction time is 2.3 seconds. Calculate his stopping distance in metres to one decimal place.
Hermione's car has a braking distance of 81 metres and Hermione's reaction time is 2.8 seconds. Calculate her stopping distance in metres to one decimal place.
What is the distance in metres between the two cars after they stop? Round your answer to one decimal place.
For a driver travelling in a car at speed V, in metres per second, the reaction time distance, D, can be given by the formula D = 2.9 V.
Calculate the reaction time distance in metres if the car is travelling at 40 \text{ km/h}. Round your answer to one decimal place.
Calculate the speed of a vehicle, in \text{km/h}, if the reaction time distance is 62 metres. Round your answer to one decimal place.
For a driver travelling in a car at speed V, in metres per second, the stopping distance can be given by the formula D = 1.5 V + \dfrac{V^{2}}{13.72}.
Calculate the stopping distance, to one decimal place, for a car travelling:
At the speed limit of 40 \text{ km/h}.
At 5 \text{ km/h} over the speed limit.
Consider the following graph:
What is the increase in stopping distance for a car moving at 80 \text{ km/h} when the road is wet, compared to when it is dry?
What is the increase in stopping distance for a car moving at 90 \text{ km/h} when the road is wet, compared to when it is dry?
Noah normally drives at the speed limit, but when the road is wet he reduces his speed by 10 \text{ km/h}, to make sure his stopping distance is the same, or less, compared to a dry road. For which speed limits does this strategy not work?
The following equation determines the duration of time, t hours, required for a person to stop consuming alcohol in order to reach zero blood alcohol content: t = \dfrac{BAC}{0.015}.
How long would a person with a BAC of 0.03 have to wait for their blood alcohol content to drop to zero? Round your answer to two decimal places.
How long would a person with a BAC of 0.10 have to wait for their blood alcohol content to drop to zero? Round your answer to two decimal places.
To calculate the number of standard drinks we use the formula N = 0.789 \times V \times A where V is the volume of the drink in litres and A is the percentage of alcohol (alc/vol) in the drink.
Calculate the number of standard drinks in a 375 \text{ mL }bottle of mid-strength beer that has an alcohol content of 3.5\% alc/vol to one decimal place.
Calculate the number of standard drinks in a 150 \text{ mL }glass of champagne that has an alcohol content of 12\% alc/vol to one decimal place.
Calculate the number of standard drinks in a 375 \text{ km/h }can of pre-mix drink that has an alcohol content of 7\% alc/vol to one decimal place.
The following formulas are used to calculate blood alcohol content (BAC):
BAC_{male}=\dfrac{10 N - 7.5 H}{6.8 M} \qquad BAC_{female}=\dfrac{10 N - 7.5 H}{5.5 M}where N is the number of standard drinks consumed; H is the number of hours of drinking; and M is the person's mass in kilograms. (Questions 32 to 35 require the use of these formulas.)
Bill is an adult male who weighs 87 \text{ kg} and has consumed 4 standard drinks in 4 hours. Calculate his blood alcohol content correct to three decimal places.
Oprah is an adult female that weighs 74 \text{ kg} and has consumed 3 standard drinks in 4 hours. Calculate her blood alcohol content correct to three decimal places.
Determine who has the higher BAC given the following conditions.
Jack and Beth both drink the same number of drinks, over the same time frame, and have the same mass.
Jack and Aaron both drink the same number of drinks over the same time frame but Aaron is heavier.
Beth and Sophia both drink the same number of drinks and have the same mass, but Beth started drinking one hour earlier.
State whether the following conditions could result in a higher blood alcohol content than the BAC formula predicts.
Their drinks were highly carbonated.
They started drinking after 6 pm.
They are not fit and healthy.
They haven't eaten recently.
They recently ate a large meal.
They drank heavily three days ago.
To calculate the number of standard drinks, N, a person has consumed we use the formula:
N = 0.789 \times V \times Awhere V is the volume of the drinks in litres, and A is the percentage of alcohol (\% alc/vol) in the drinks.
For each of the following people, calculate:
The number of standard drinks, N, they have consumed correct to one decimal place.
Their blood alcohol content, BAC, correct to three decimal places.
A male weighs 76\text{ kg}, and drinks three 275 \text{ mL} bottles of low strength beer with an alcohol content of 2.7\% alc/vol, over 3 hours.
A female with a mass of 53 \text{ kg}, who drinks three 425 \text{ mL} bottles of full strength beer with an alcohol content of 4.8\% alc/vol, over 3 hours.
Judy goes to a party and consumes four 275 \text{ mL} bottles of a pre-mix drink, labelled as 5\% alc/vol, over 2 hours.
In many places, new drivers such as learners and provisional drivers must have a blood alcohol content (BAC) of zero to be able to legally drive a car.
Oliver weighs 58 \text{ kg} and drinks 5 standard drinks in 3 hours. Katrina weighs 75 \text{ kg} and drinks 4 standard drinks in 3 hours.
Determine the BAC of Oliver, correct to three decimal places.
Determine the BAC of Katrina, correct to three decimal places.
To calculate the duration of time required before a person's BAC returns to zero, we use the formula: t = \dfrac{BAC}{0.015}.
Calculate the duration of time required after Oliver stops consuming alcohol before his BAC returns to zero. Round your answer to two decimal places.
Calculate the duration of time required after Katrina stops consuming alcohol before her BAC returns to zero. Round your answer to two decimal places.
If both Oliver and Katrina are on their provisional license, who is able to legally drive first?
It is commonly considered safe to drink two drinks in the first hour and one drink per hour after that. Lachlan drinks two 375 \text{ mL} bottles in the first hour and one every hour after that for three hours.
If Lachlan drinks light beer with a 2.7\% alc/vol, how many standard drinks, N, has he consumed?
Determine the BAC of Lachlan (correct to three decimal places) if his mass is 81 \text{ kg}.
If Lachlan drank full strength beer instead of light beer, he would consume 7.1 standard drinks. Determine his {BAC} in this case, correct to three decimal places.