SOLUTION: A backpacker hiking into the wilderness area walked 9 miles at a constant rate and then reduced this rate by 1 mph. Another 4 miles was hiked at this reduced rate. The time require

Question 252581: A backpacker hiking into the wilderness area walked 9 miles at a constant rate and then reduced this rate by 1 mph. Another 4 miles was hiked at this reduced rate. The time required to hike the 4 miles was 1 hour less than the time required to walk the 9 miles. Find the rate at which the hiker walked the first 9 miles.
Found 3 solutions by stanbon, drk, JimboP1977:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A backpacker hiking into the wilderness area walked 9 miles at a constant rate and then reduced this rate by 1 mph. Another 4 miles was hiked at this reduced rate. The time required to hike the 4 miles was 1 hour less than the time required to walk the 9 miles. Find the rate at which the hiker walked the first 9 miles.
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1st segment DATA:
distance = 9 miles ; rate = x mph ; time = d/r = 9/x hrs
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2nd segment DATA:
distance = 4 miles ; rate = x-1 mph ; time = d/r = 4/(x-1) hrs
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Equation:
1st seg. time - 2nd seg. time = 1 hr
9/x - 4(x-1) = 1 hr
9(x-1) - 4x = x(x-1)
9x-9 - 4x = x^2-x
x^2 -6x +9 = 0
(x-3)^2 = 0
x = 3 mph (rate for the 1st segment)
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Cheers,
Stan H.
Answer by drk(1908)   (Show Source): You can put this solution on YOUR website!
Lets set up a quick rate x time = distance table:
Rate . . . Time . . . distance
r . . . .. . . . 9/r . . . . . . . 9
(r-1) . . . . .4/(r-1) . . . . 4
The time required to hike the 4 miles was 1 hour less than the time required to walk the 9 miles is translated as:
9/r - 1 = 4/(r-1).
we solve for r by multiplying by r(r-1) on both sides:
9(r-1) -r(r-1) = 4r
9r - 9 - r^2 + r = 4r
r^2 - 6r + 9 = 0
(r-3)(r-3) = 0
r = 3 mph for the first 9 miles.
Answer by JimboP1977(311)   (Show Source): You can put this solution on YOUR website!
(1)

Take 1 away from both sides of equation (1).

so x = 3
The rate is 3mph.

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