New Zealand
Level 6 - NCEA Level 1

# Calculate Speed/Distance/Time

Lesson

When calculating speed, you may occasionally need to convert between units of length or between units of time. This becomes a little trickier when you need to convert between different speeds.

## Kilometres per hour to metres per second

You need to remember to change both of the units here. Kilometres are converted to metres by multiplying by $1000$1000. Hours are converted to seconds by multiplying by $3600$3600.

If you wanted to convert 4 kilometres per hour to metres per second you would need to do:

$\frac{4\times1000}{1\times3600}$4×10001×3600 = $\frac{4000}{3600}$40003600 = $1.1111$1.1111 m/s

Sometimes when I work out these conversions I think about it vertically, and I concentrate on the units.  I can do it piece by piece.

Here is the same question done in a different way.

 $4$4 km/h $=$= $4000$4000metres/$60$60 minutes writing the $4$4 km as meters, and the $1$1 hour as minutes $=$= $400$400 meters / $6$6 minutes simplifying a little $=$= $200$200 meters / $3$3 minutes simplifying a bit more $=$= $200$200 meters / 180 seconds because $3$3 minutes is the same as $3\times60$3×60 seconds $=$= $20$20 meters / $18$18 seconds simplify $=$= $10$10 meters / $9$9 seconds simplify $=$= $1.11$1.11m/s calculate

#### Worked Examples

##### Question 1

Convert the following amounts into the units required, writing your answers correct to 2 decimal places where necessary:

1. $2500$2500 metres into kilometres

2. $2100$2100 seconds into minutes

3. $45$45 km/h into m/s

4. $7.562$7.562 kilometres into metres

5. $6.85$6.85 hours into seconds

6. $14$14 m/s into km/h

##### Question 2

If a sugar glider possum travels $6$6 km at a speed of $15$15 km/hr, how long will it take the animal to cross the whole distance?

##### Question 3

A dog travels $42$42 km in $1.4$1.4 hours.

1. At what speed is it travelling?

### Outcomes

#### NA6-1

Apply direct and inverse relationships with linear proportions

#### 91026

Apply numeric reasoning in solving problems