Question

6 of 6

Lena and Ras drive to work.
Lena drives 24 miles in 1.5 hours.
Ras drives 36 km in 1 hour 15 min.
Work out the difference between their average speeds in km/h.
1 mile = 1.6 km
km/h

Answer 1

3.2 km/h

Explanation:

1. Approach

The average speed is the rate at which one travels. It can be found by diving the total distance traveled over the total time it took to cover that distance. In essence, the following formula can be used to find the average speed:

`(total\ distance)/(total\ time)=average\ speed`

In this situation, one is asked to find the difference between two people's average speed. One is given the following information:

Lena: 24 miles 1.5 hours

Ras: 36km 1 hour 15 minutes

First, convert all of the numbers into the correct units (km) and (hours). Then find the average speed for each person. Finally, subtract the smaller speed from the larger speed to find the difference in the average speeds.

1. Find Lena's average speed

The problem asks one to find the average speed in the units (km/h). However, the distance Lena covered is given in (miles). Therefore, one has to multiply it by the conversion factor (1.6) in order to convert it from (miles) to (km).

24miles * 1.6 = 38.4

Now find the average speed by using the formula:

`(total\ distance)/(total\ time)=average\ speed`

Substitute,

`(38.4)/(1.5)\\\\=25.6`

2. Find Ras's average speed

Use a similar approach to work out Ras's average speed, as was used to find Lena's average speed. Since Ras's time spent is given in both hours and minutes, one must convert it to just minutes. There are (60) minutes in an hour, thus, one can rewrite the number as the following:

`1\ hour \ \ 15\ minutes= 1 (15)/(60)\ hours = (75)/(60)\ hours`

Now find the average speed:

`(total\ distance)/(total\ time)=average\ speed`

Substitute,

`(36)/((75)/(60))\\\\=28.8`

3. Find the difference between the speeds

Since Ras's speed is greater, subtract Lena's speed from Ras's speed.

Ras - Lena

= 28.8 - 25.6

= 3.2