SOLUTION: With a tail wind, a plane flew 1000 miles in 2 hours. The plane, flying directly against that same wind, required 2.5 hours for the return trip. Find the speed of the plane and the

Question 1174890: With a tail wind, a plane flew 1000 miles in 2 hours. The plane, flying directly against that same wind, required 2.5 hours for the return trip. Find the speed of the plane and the speed of the wind.
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

The speed with the wind was 1000/2 = 500 mph.

The speed against the wind was 1000/2.5 = 400 mph.

if you want to (or need to) solve that algebraically, you can solve the system of equations
p+w = 500 (plane speed plus wind speed)
p-w = 400 (plane speed minus wind speed)

I leave it to you to finish solving the problem by that formal method.

There are a wide range of problems which lead to a similar situation -- the sum of two numbers is A and their difference is B; find the two numbers.

A fast common sense solution is to realize that one of the numbers is halfway between the two given numbers. An easy way to see this is to picture the numbers on a number line. You start at one number and go one direction to get to A; you start at the same number and go the opposite direction to get to B. That means the number you started at is halfway between A and B.

So for this problem, the speed of the plane is halfway between 400 and 500, which is 450; then of course the speed of the wind is the difference between 450 and either 400 or 500.

ANSWERS:
plane speed 450 mph
wind speed 50 mph

Answer by josgarithmetic(39615) (Show Source): You can put this solution on YOUR website!
Same as if to describe
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With a tail wind, a plane flew 1000 miles in 2 hours (500 miles per hour). The plane, flying directly against that same wind, required 2.5 hours for the return trip (400 miles per hour).
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Simple to solve, ready for Elimination Method.
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