Question

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 ?

Answer 1

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

Explanation:

Define
`color(white)("XXX")t_1=` time spent going up hill
`color(white)("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
`color(white)("XXX")35t_1 = 66t_2`

Suppose that it was a really long hill that took `66" hr"` to go up.
In this case it would take `35 " hr"` to go down.
The total time taken would be `66+35 = 101 " 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 " hr"` was simply a value with which it was easy to perform the calculations.