Question

Two planes make a 900 mile flight, one flying 50 miles per hour faster than the other. The quicker plane makes the trip 3 hours faster. How long did it take the slower plane to complete the flight?

Answer 1

let the speed of the slower plane be x mph, then
1000/x - 1000/(x+75) = 3

multiply across by x(x+75)
1000(x+75) - 1000x = 3x(x+75)

collect terms & simplify
3x² + 3*75x - 1000*75 = 0
x² +75x - 25,000 = 0

(x+200)(x-125) = 0

take the positive value,
x = 125 mph
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Faster plane:
200 mph
5 hours

Slower plane
125 mph
8 hours