# 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

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 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(57239)   (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. ------- 1st segment DATA: distance = 9 miles ; rate = x mph ; time = d/r = 9/x hrs -------------- 2nd segment DATA: distance = 4 miles ; rate = x-1 mph ; time = d/r = 4/(x-1) hrs ------------------- 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) ====================================== 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(308)   (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.