Question 497136
Jack and Jill went up the hill at a rate of 8 units per minute. 
They came tumbling down at a rate of 8 units per second.
 What was their average rate, in units per minute, for the round trip?
:
Find the tumbling down rate in units/min 
8*60 = 480 units per minute
:
Let d = the one-way distance
Let a = average units/min for the round trip (2d)
:
Write a time equation; time = dist/rate
:
Up time + tumble down time = total time
{{{d/8}}} + {{{d/480}}} = {{{(2d)/a}}}
:
multiply by 480a, results
60ad + ad = 960d
61ad = 960d
we don't care about d, divide thru by d, to eliminate it.
 61a = 960
a = {{{960/61}}}
a = 15.738 units/minute average rate
:
:
Confirm this, let the one way dist = 1, find the times
{{{1/8}}} + {{{1/480)}}} = {{{2/15.738)}}}
use decimals here
.125 + .002 = .127, confirms our average speed of 15.738 units/min