SOLUTION: A plane traveled 2464 miles to Philadelphia and back. With the wind to Philadelphia, it took 14 hours. Into the wind on the way back, it took 16 hours. How fast is the plane travel

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Question 1060222: A plane traveled 2464 miles to Philadelphia and back. With the wind to Philadelphia, it took 14 hours. Into the wind on the way back, it took 16 hours. How fast is the plane traveling when there is no wind? What is the wind speed?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
                      SPEED        TIME        DISTANCE

TO PHILADELPHIA       r+w           14           2464

FROM PHIL.            r-w           16           2464


UNKNOWNS: r for speed if no wind, w speed of the wind;
system%28p=14%2Cb=16%2Cd=2464%29

system%28%28r%2Bw%29p=d%2C%28r-w%29b=d%29

system%28pr%2Bpw=d%2Cbr-bw=d%29

pw=d-pr
w=%28d-pr%29%2Fp
-
br-b%28%28d-pr%29%2Fp%29=d
bpr-b%28d-pr%29=dp
bpr-bd%2Bbpr=dp
2bpr-bd=dp
2bpr=dp-db
highlight%28r=%28dp-db%29%2F%282bp%29%29--------substitute the given values and evaluate r. When you have this value use w=%28d-pr%29%2Fp to evaluate w.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
A plane traveled 2464 miles to Philadelphia and back. With the wind to Philadelphia, it took 14 hours. Into the wind on the way back, it took 16 hours. How fast is the plane traveling when there is no wind? What is the wind speed?
If you're CONFUSED by the response of the other person, then this is the way to do the problem:

Let speed in still air be S, and wind speed, W

Average speed during trip to PA: matrix%281%2C4%2C+%222%2C464%22%2F14%2C+or%2C+176%2C+mph%29

Average speed during return trip: matrix%281%2C4%2C+%222%2C464%22%2F16%2C+or%2C+154%2C+mph%29

We then get the following system of equations for the average speed: 

Add these 2 and solve for S: the speed of the plane in still air

Substitute the value for S into any of the 2 equations, and solve for W, the wind speed!

Voila!! Done!! It's that simple....nothing complex, and certainly without "150" different variables