# It took David an hour to ride 20 km from his house to the nearest town. He then spent 40 minutes on the return journey. What was his average speed?

##### 1 Answer

#### Explanation:

The **average speed** is simply the rate at which the *distance* travelled by David varies **per unit of time**.

#"average speed" = "distance covered"/"unit of time"#

In your case, you can take a unit of time to mean **hour**. Since you know that

#"1 h = 60 min"#

you can say that David needed

#40 color(red)(cancel(color(black)("min"))) * "1 h"/(60color(red)(cancel(color(black)("min")))) = 2/3color(white)(.)"h"#

to make the return trip.

Now, notice that on his way from his house to the town hall, David travels **hour**. This means that his average speed for the *first part* of the journey will be

#"average speed"_ 1 = "20 km"/"1 h" = "20 km h"^(-1)#

Since it takes **less** than an hour for David to complete the return trip, you can say that his average speed for the *return trip* will be **higher** *more distance* per unit of time on his return trip.

More specifically, David will cover

#1 color(red)(cancel(color(black)("h"))) * "20 km"/(2/3color(red)(cancel(color(black)("h")))) = "30 km"#

in **hour** on his return trip, so his average speed will be

#"average speed"_2 = "30 km h"^(-1)#

So, you know the average speed for the first trip and the average speed for the return trip, so you can simply take the *average* of these two values, right? **Wrong**!

It is **absolutely crucial** to avoid going

#color(red)(cancel(color(black)("average speed" = ("20 km h"^(-1) + "30 km h"^(-1))/2 = "25 km h"^(-1))))#

because you will get an incorrect answer **per unit of time**.

You know that you have

#"total distance = 20 km + 20 km = 40 km"# #"total time" = "1 h" + 2/3color(white)(.)"h" = 5/3color(white)(.)"h"#

So if David covers **hours**, how many kilometers does he cover in **hour**?

#1 color(red)(cancel(color(black)("h"))) * "40 km"/(5/3color(red)(cancel(color(black)("h")))) = "24 km"#

Therefore, you can say that David has an average speed of

#"average speed" = color(darkgreen)(ul(color(black)("24 km h"^(-1))))#

I'll leave the answer rounded to two **sig figs**, but don't forget that your values justify only one significant figure for the answer.

This is why the equation for *average speed* is given as

#"average speed" = "total distance"/"total time"#

In your case, you have

#"average speed" = "40 km"/(5/3color(white)(.)"h") = 40/(5/3)color(white)(.)"km"/"h" = "24 km h"^(-1)#