SOLUTION: a man bicycles 5 mph faster than he walks. He bicycles 24 miles and then hikes back along the same route in 11 hours. How fast does he walk?

Question 282952: a man bicycles 5 mph faster than he walks. He bicycles 24 miles and then hikes back along the same route in 11 hours. How fast does he walk?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
5x+x=24
6x=24
x=4 mph walking
5x=20 mph riding
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
a man bicycles 5 mph faster than he walks. He bicycles 24 miles and then hikes back along the same route in 11 hours. How fast does he walk?

Let the speed that he walks be W.

Then the speed that he bikes at is W + 5, since he bikes 5 mph faster than he walks

His time to walk 24 miles (end leg of trip) would then be: , and his time to bike 24 miles (1st leg of trip) would be:

Since he does both ends of the trip in 11 hours, then we'll have:

---- Multiplying by LCD W(W + 5)

(11W + 40)(W - 3) = 0

11W = - 40 (ignore, as speed CANNOT be a negative value)

Therefore, W, or his walking speed = , and since B, or his biking speed = W + 5, then he bikes at: mph.
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