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 $275 m/h$ $275" m/h"$ and that of the wind, $25 m/h.$ $25" m/h."$

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

and that of the wind, $w$ $w$ .

During the trip of $1000 miles$ $1000" miles"$ 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 $(p - w) m/h.$ $(p-w)" m/h."$

Now, $speed \times time = distance,$ $"speed"xx"time"="distance,"$ 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.!