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
#"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
#"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 specifically, David will cover
#1 color(red)(cancel(color(black)("h"))) * "20 km"/(2/3color(red)(cancel(color(black)("h")))) = "30 km"#
in
#"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
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
#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)#