mike spent 3 hours biking up winding stair mountain rested f

mike spent 3 hours biking up winding stair mountain, rested for 45 minutes,
and biked back 2 hours.
how far did he bike if his rate of ascent was 2.5 miles less than his rate of decent?

Solution

First find the speed:
:
Let s = speed descending
then
(s-2.5) = speed ascending
:
Dist up and back are the same. Write a distance equation: Dist = time * speed
3(s-2.5) = 2s
3s - 7.5 = 2s
3s - 2s = 7.5
s = 7.5 mph, descending speed
then
5 mph, ascending speed
:
Find the dist:
5 * 3 = 15 mi
and
2 * 7.5 = 15 mi
:
He biked a total of 30 mi up and back