A search plane has a cruising speed of 250 miles per hour an

A search plane has a cruising speed of 250 miles per hour and carries enough fuel for at most 5 hours of flying. If there is a wind that averages 30 miles per hour and the direction of search is with the wind one way and agianst it the other, how far can the search plane travel?

Solution

Remember that distance traveled equals rate (speed) * time traveled or D = R*T.
The speed of the plane with the wind is 250+30=280 and against the wind is 250-30=220
We know also that the total time traveled will be 5 hours.
Let D be the total distance traveled and D/2 the distance traveled either way.
Let T be the time traveled against the wind.
Then 5-T is the time traveled with the wind.
We have then:
(1.) 220*T + (5-T)*280 = D
and for one way
220*T = D/2 or
(2.) D = 440*T
Subtitute 440*T for D in the first equation:
220*T + (5-T)*280 = 440*T
220*T + 5*280 - 280*T = 440*T
220*T + 1400 - 280*T = 440*T
500*T = 1400
T = 14/5 hours
Substitute 14/5 for T in the second equation:
D = 440*14/5 = 88*14 = 1232 miles