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 ?

1 Answer
Sep 7, 2015

Answer:

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.