Wind speed and distance? URGENT!!!!!!?

Question

A plane whose air speed is 150 mi/h flew from Abbot to Blair in 2 hours with a tail wind. On the return trip against the same wind, the plane was still 60 mi from Abbot after two hours. Find the wind speed and the distance between Abbot and Blair.

How do I calculate this?????Please be clear, thanks

Answer 1

You have two rates in action together: the air speed of the plane and the wind speed.

Air speed of the plane = 150
w = wind speed

Then with the tail wind, the plane travels (150 + w) mi/h.
Returning, it travels (150 - w) mi/h.

So using d = r*t,
d = (150 + w)*2 for going there. Then
d - 60 = (150 - w)*2 or
d = (150 - w) * 2 + 60 for returning.
Since both equations now start with "d=", set them equal to each other and solve for w.
(150 + w)*2 = (150 - w) * 2 + 60
300 + 2w = 300 - 2w + 60
4w = 60
w = 15

Then use the first equation to solve for d:
d = (150 + 15)*2
d = 165*2
d = 330 miles

You can check using the returning equation if you would like.

I hope this helps!

Answer 2

let wind speed = w

distance = 2 (150 + w) = 300 + 2w

distance - 60 = 2 (150 - w) = 300 - 2w

so distance = 360 - 2w = 300 + 2w

4w = 60

w = 15 mph

distance = 330 miles