5.05 Rates

Write the following as a unit rate:

A car travels 320\text{ km} in 4 hours.

A tap fills up a 240 litre tub in 4 hours.

A tap fills up a 259 litre tub in 7 hours. Find the rate of water flow of the tap in litres per hour.

A toy manufacturer makes 720 toys in 9 hours.

A toy manufacturer makes 165 toys in 5 hours. At what rate are the toys made per hour?

Justin earns \$420 in 6 hours. Find Justin's hourly rate.

Luke earns \$328 in 8 hours. Find Luke's hourly rate.

Tricia reads 20 pages of her book in 2 hours. Find her reading rate of pages per hour.

Luke writes 900 words in 20 minutes. Find Luke's writing speed in words per minute.

Tina burns 640 calories by jogging 8 kilometres. Find the rate at which Tina burns calories per kilometre.

A plane burns 406 \text{ L} of fuel every 14\text{ km} while in the air. Express the fuel consumption as a unit rate.

A 3-episode TV series had a total run time of 69 minutes. Find the run time for a single episode.

An animator uses 12 frames for every 0.5 seconds of an animation. Find the frame rate of the animation in frames per second \text{(fps)}.

Lisa is trying to save money so she deposits \$3.20 into her bank account for every 8 coffees she purchases. How much does Lisa deposit for each cup of coffee?

Avril is running from John in a game of tag. Avril runs 30 metres every 5 seconds and John runs 21 metres every 3 seconds.

A worm takes 15 seconds to travel 20\text{ cm}.

A worm takes 20 seconds to travel 25\text{ cm}. How long does it take the worm to travel a metre?

A tap is dripping at a rate of 1000\text{ mL/hr} . A 5\text{ L} bucket is placed underneath it to catch the water.

Patricia eats 7.2 \text{ L} of ice cream in 6 minutes in an ice-cream eating contest. Patricia wants to find her rate of ice-cream consumption in millilitres per second.

A cyclist travels 70 metres per 10 seconds. Find the speed of the cyclist in metres per minute.

Tina counts 26 heart beats over a 20 second interval. Find Tina's heart rate in beats per minute (bpm).

Adam really likes apples and eats them at a rate of 4 per day.

A bus travels at a speed of 80\text{ km/hr}. How far does the bus travel in 5 hours?

Iain earns \$22 per hour working as a performer and works for 20 hours a week. Find Iain's weekly earnings.

Caitlin plays cricket over the summer holidays. Caitlin scores at a rate of 24 runs per game and there are 30 games in the season. How many runs did Caitlin score in total?

It requires 8\text{ mL} of polyethylene to create 20 plastic bags.

The height of a pool increases by 5\text{ cm} for every 10 \text{ L} of water added. After adding some water the height of the pool increased by 0.45\text{ m}. How much water was added to the pool?

The height of a pool increases by 0.3 \,\text{cm} for every litre of water added. If the height of the pool increases by 6 \,\text{cm}, how much water was added?

In 2018, the birth rate in the United States was 13 people for every 1000 in the population. For a town with a population of 39\,000, how many births would you expect there to be in that year?

In 2018, the birth rate in Japan was 7 people for every 1000 population. For a town with a population of 39\,069, how many births would you expect there to be that year?

In 2018, the birth rate in Singapore was 9 people for every 1000 in the population. For a town with a population of 24\,176, how many births would you expect there to be that year?

In 2018, the population growth of Benin was 35 per 1000. This means that for every 1000 people, the number of people at the end of the year would be 1035. For a town with a population of 640, what would you expect the population to be at the end of the year?

In 2018, the population growth of Colombia was 8 per 1000. This means that for every 1000 people, the number of people at the end of the year would be 1008. For a town with a population of 95\,000, what would you expect the population to be at the end of the year?

Tom is attending to a patient on the way to the emergency department. In the ambulance, he takes a quick measurement of the patient's heart rate, and finds it to be 36 beats per 20 seconds. An hour later, in the hospital he takes a more detailed measurement and finds the patient's heart rate to be 240 beats per 120 seconds.

The Ocean Zone theme park on the Gold Coast had 3220 people enter, and was open for 14 hours on Wednesday. On Thursday, it had 2970 people enter, and was open for 9 hours. If there are more than 270 people entering the park per hour, then Ocean Zone adds extra staff at the gate.