SOLUTION: A small plane can fly 180 miles against a 30 mph wind in the same amount of time it takes to fly 540 miles with the 30 mph wind. What is the ground speed of the plane?

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Question 168237: A small plane can fly 180 miles against a 30 mph wind in the same amount of time it takes to fly 540 miles with the 30 mph wind. What is the ground speed of the plane?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The times are the same for both trips, so
t+=+d%5B1%5D+%2F+r%5B1%5D
t+=+d%5B2%5D+%2F+r%5B2%5D
given:
d%5B1%5D+=+180 mi
d%5B2%5D+=+540 mi
30 = mi/hr windspeed
Let p= ground speed of the plane
t+=+180+%2F+%28p+-+30%29
t+=+540+%2F+%28p+%2B+30%29
Since time is the same in both equations
180%2F%28p+-+30%29+=+540+%2F+%28p+%2B+30%29
Multiply both sides by %28p+-+30%29%2A%28p+%2B+30%29
180%2A%28p+%2B+30%29+=+540%2A%28p+-+30%29
180p+%2B+5400+=+540p+-+16200
360p+=+21600
p+=+60
The ground speed of the plane is 60 mi/hr
check:
180%2F%28p+-+30%29+=+540+%2F+%28p+%2B+30%29
180%2F%2860+-+30%29+=+540+%2F+%2860+%2B+30%29
180%2F30+=+540%2F90
6+=+6
OK