find the speed ofeach plane

Question

 A turbo-jet flies 50mph faster than a super-prop plane. If a turbo-jet goes 2000mi in 3 hr less time than it takes the super-prop to go 2800 mi, find the speed of each plane

Answer 1

Let P = speed of prop plane

then P + 50 = speed of jet

 

Let t = time prop plane flies and t -3 = time jet plane flies

 

Pt = 2800 => P = 2800/t

 

(P + 50)(t - 3) = 2000

 

[(2800/t) + 50)(t-3) = 2000

 

(2800 + 50t)(t-3) = 2000t

 

2800t + 50t² - 8400 -150t = 2000t

 

Collect terms and divide by 50

t² + 13t -168 = 0

The quadratic formula gives t=8 (and an extraneous negative root)

 

P = 2800/8 = 350

 

P+50 (the speed of the jet plane) = 400

 

You should substititue these values back into the original problem to make sure they are correct.

 

Note: On review this looks like a complicated set up.  I believe it is correct but someone else may come up with a less complicated solution.

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