A girl goes up a ski lift at a speed of 4 MPH and skis down

A girl goes up a ski lift at a speed of 4 MPH and skis down the slope at a speed of 24 MPH. If the ski slope is the same length as the ski lift and if we ignore any time spent at the top of the hill, what is her average speed for the round trip?

Solution

Let x = length of ski slope
then
.
time going up = d/r = x/4
time going down = d/r = x/24
.
total distance = 2x
.
Average speed = \"total distance\"/\"total time\"
Average speed = 2x/(x/4 + x/24)
Average speed = 2x/(6x/24 + x/24)
Average speed = 2x/((6x+ x)/24)
Average speed = 2x/(7x/24)
Average speed = 48x/7x
Average speed = 48/7
Average speed = 6.86 mph