With a head wind, a plane traveled 1000 miles in 4 hours. With the same wind as a tail wind, the return trip took 3 hours and 20 minutes. How do you find the speed of the plane and the wind?

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Answer 1 · 2017-11-11T06:58:52

Speed of the plane #275" m/h"# and that of the wind, #25" m/h."#

Suppose that the speed of the plane is #p" miles/hour (m/h)"#

and that of the wind, #w#.

During the trip of #1000" miles"# of the plane with a head wind,

as the wind opposes the motion of the plane, and as such, the

effective speed of the plane becomes #(p-w)" m/h."#

Now, #"speed"xx"time"="distance,"# for the above trip, we get,

#(p-w)xx4=1000, or, (p-w)=250.............(1).#

On the similar lines, we get,

#(p+w)xx(3" hour "20" minutes)"=1000......(2).#

Note that,

#(3" hour "20" minutes)"=(3+20/60" hour")=10/3" hour."#

#:. (2) rArr (p+w)(10/3)=1000, or, (p+w)=300....(2').#

#(2')-(1) rArr 2w=50 rArr w=25.#

Then, from #(1),# we get, #p=w+250=275,# giving, the desired

Speed of the plane #275" m/h"# and that of the wind, #25" m/h."#

Enjoy Maths.!