SOLUTION: After driving 126mi, Syd found that the drive would have taken 1 hr. less time by increasing the speed by 8 mph. What was the actual speed?

Question 786176: After driving 126mi, Syd found that the drive would have taken 1 hr. less time by increasing the speed by 8 mph. What was the actual speed?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
After driving 126mi, Syd found that the drive would have taken 1 hr. less time by increasing the speed by 8 mph. What was the actual speed?
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Actual DATA:
distance = 126 miles ; rate = x mph ; time = 126/x hours
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"If" DATA:
distance = 126 miles ; rate = x+8 mph ; time = 126/(x+8) hours
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Equation:
126/x - 126/(x+8) = 1 hr
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126(x+8) - 126x = x(x+8)
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x^2 + 8x - 8*126 = 0
x = 36 mph (actual speed)
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Cheers,
Stan H.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!

In the actual case:

In the other case:

By substitution:

Multiply both sides by

Use quadratic formula

and, since

The actual speed was 28 mi/hr
check:

OK

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