A plane travels with a tail wind 100 miles to the nearest to

A plane travels with a tail wind (100) miles to the nearest town in (60) minutes. The plane then travels back (100) miles with a head wind. The travel time is (40) min more than the first trip. What is the speed of the wind, and the speed of the plane?

Solution

Let the speed of the plane in still air be x mph
Let the speed of the wind be y mph

Then in the first case,
x+y=the total speed
total speed=total distance/total time
=100/1
=100 mph

x+y=100

Now in the second case,
x-y=second speed
second speed=same distance/more time
=100/(1+40/60)
=100/(1+2/3)
=100/(5/3)
=60 mph

x-y=60

Now we have two equations
x+y=100
x-y=60
adding the two,
2x=160
x=80 mph

y=100-x=100-80=20 mph

Therefore,speed of wind=20 mph and speed of plane is 80 mph
Hope this helps