# A car travels up a hill at a constant speed of 35 km/h and returns down the hill at a constant speed of 66 km/h. How to calculate the average speed for the round trip ?

Sep 7, 2015

Average speed $= 45.74$ km/hr (approximately)

#### Explanation:

Define
$\textcolor{w h i t e}{\text{XXX}} {t}_{1} =$ time spent going up hill
$\textcolor{w h i t e}{\text{XXX}} {t}_{2} =$ time spent going down hill

Distance going up hill = (35 " km")/("hr")*t_1" hr"

Distance going down hill = (35 " km")/("hr")*t_1" hr"

Since the distances are equal
$\textcolor{w h i t e}{\text{XXX}} 35 {t}_{1} = 66 {t}_{2}$

Suppose that it was a really long hill that took $66 \text{ hr}$ to go up.
In this case it would take $35 \text{ hr}$ to go down.
The total time taken would be $66 + 35 = 101 \text{ hr}$
and
the total distance covered would be
color(white)("XX")(35 " km")/("hr")*66" hr" + (35 " km")/("hr")*35" hr" = 4620 " km"
and
the average speed would be (4620 " km")/(101 " hr") = 45.74 "km/hr"

Notice that the proportions remain the same no matter what amount of time you assume it would take to go up the hill. $66 \text{ hr}$ was simply a value with which it was easy to perform the calculations.