A twin engine plane can fly 800 miles in the same time that.....?

Question

A twin-engine plane can fly 800 miles in the same time that it takes a single engine plane to fly 600 miles. The rate of the twin engine plane is 50 mph faster than that of the single-engine plane. Find the rate of the twin-engine plane

Answer 1

time = distance/rate, times are equal, so

800/r1 = 600/r2 ........and r1 = r2 + 50

800/(x+50) = 600/x
8/(x+50) = 6/x
8x = 6x + 300
2x = 300
x = 150 mph
x+50 = 200 mph .... twin engine rate

Answer 2

Call the rates R2 for the 2-engine plane and R1 for the one-engine. Then R2 = R1 + 50 (given), and R2 = 4/3R1 (because 800 = 600*(4/3).

if you plug the first, simpler equation into the second, you get R1 + 50 = 4/3 R1. But since we're trying to find R2, rewrite the first equation as R1 = R2 - 50 and you can plug in to get R2 = 4/3(R2-50). Distribute the 4/3 and you get R2 = 4/3R2 - 200/3. Subtract 4/3R2 from each side and you get -R2/3 = -200/3. Multiply both sides by -3 and you get R2 = 200.

Check the answer. If the twin-engine plane flies 200 mph, it takes it 4 hours to fly 800 miles. The single-engine plane flies 50 mph slower, or 150 mph, so it takes it four hours to fly 600 miles. The answer checks out.

The twin-engine plane flies 200 mph.