SOLUTION: Rob drives 550 miles home in one hour less than it takes Mary to drive the same route. Rob's average speed is 8 mph faster than Mary's. How fast does each drive.

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Question 28741: Rob drives 550 miles home in one hour less than it takes Mary to drive the same route. Rob's average speed is 8 mph faster than Mary's. How fast does each drive.

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
MAry's speed = x
Rob's = x+8
Total milies driven by them both = 550.
time taken = one hour less = -1 so x+8-x=1

Equation:
550%2F%28x%2B8%29-550%2Fx=1
550[(x+8)-(x)]=(x)(x+8)
550%288%29=x%5E2%2B8x
4400=x%5E2%2B8x
x%5E2%2B8x-4400=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%28-8%2B-sqrt%28%288%5E2%29-4%2A1%2A-4400%29%29%2F%282%2A1%29
simplfy get two solutions.
Delete the negative answer.
x=4%282sqrt%2869-1%29%29
x=58 (rounded)
58+8=66

Hence, Mary's speed is 58mph and Rob's speed is 66 mph.
Paul.