Question 149374
A plane which can fly 100 miles an hour in still air can fly 500 miles with a wind which is blowing at a certain rate in 5/8 of the time it would require to fly 500 miles against a wind blowing at the same rate. What was the rate of the wind?
:
Let x = the rate of the wind
then
(100-x) = speed against the wind
and
(100+x) = speed with the wind
:
Write a time equation: Time = {{{dist/speed}}}
:
With the wind time = Against time * {{{5/8}}}
{{{500/((100+x))}}} = {{{500/((100-x))}}} * {{{5/8}}}
{{{500/((100+x))}}} = {{{2500/(8(100-x))}}}
{{{500/((100+x))}}} = {{{2500/((800-8x))}}}
Cross multiply:
2500(100+x) = 500(800-8x)
:
250000 + 2500x = 400000 - 4000x
;
2500x + 4000x = 400000 - 250000
:
6500x = 150000
x = {{{150000/6500}}}
x = 23.1 mph, the rate of the wind
:
:
Check solution, find the time for each trip
{{{500/123.1}}} = 4.06 hrs
{{{500/76.9}}} * {{{5/8}}} = 4.06 hr