Two planes just took off from Charlotte NC. The first plane is traveling 1.5 times as fast as the second plane. After traveling in the same direction for 2.5 hours, they are 127.5 miles apart. What is the average speed of each plane?

Givens

Slower plane

r = r

t = 2.5 hours

d = d

Faster Plane

r_faster = 1.5 * r

t = 2.5 hours

d1 = d + 127.5

The time is the same for both

t = d/r

d1/r1 = d/r

(d + 127.5) / 1.5r = d/r Multiply each side by r

(d + 127.5) / 1.5 = d Multiply both sides by 1.5

d + 127.5 = 1.5d Subtract d from both sides.

127.5 = 1.5d - d

127.5 = 0.5d Divide by 0.5

127.5 / 0.5 = d

255 = d

Now you can go back and figure out the rates.

First find d1

d1 = d + 127.5

d1 = 255 + 127.5

d1 = 382.5

Rate of the slower plane

d = 255

t = 2.5 hours

r = d/t

r = 255/2.5

r = 102 miles per hour.

Faster plane

d1 = 382.5 miles

t = 2.5 hours

r1 = d/t

r1 = 382.5/2.5 = 153 miles per hour.