rate of passenger boat --- x mph
rate of freighter --------- x-6 mph
2592/(x-6) - 2592/x = 72 , assuming they travel 24 hours per day
multiply each term by x(x-6)
2592x - 2592(x-6) = 72x(x-6)
2592x - 2592x + 15552 = 72x^2 - 432x
72x^2 - 432x - 15552 = 0
9x^2 - 54x - 1944= 0
(x - 18)(9x + 108) = 0
x = 18 or x is a negative
the rate of the passenger boat was 18 mph
the rate of the freighter was 12 mph
check
2592/18 = 144 hrs
2592/12 = 216441 hrs
difference is 216-144 = 72
My answer of x = 18 is correct
A passenger boat which travels 6 mph faster than a freighter required 3 days less time to make a trip of 2592 miles. Find the rate of the passenger boat.
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