Rate Problem: Bicycle and Walking?

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fantasy24football

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A man bicycles 5 mph faster than he can walk. He bicycles 24 miles and walks back along the same route in 11 hours.

How fast does he walk?
i think the 11 hours applies both to walking and biking.
3 mph is correct but i'm not sure how to solve to get that
 
let the rate of walk = x mph

The rate of cycling = x + 5

time taken for walking = 24/x

time taken for cycling = 24 /(x + 5)

so 24/ x + 24 / x+ 5 = 11

24(1 / x + 1 / x+ 5 ) = 11

24( x + 5 + x ) / x (x + 5) = 11

24 (2x + 5) = 11(x)(x+5)

48x + 120 = 11x^2 + 55x

11x^2 + 7x - 120 = 0

11x^2 + 40x - 33x - 120 = 0

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

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

x = 3

he can walk at the rate of 3 mph
 
3 mph.

He bikes at 8 mph for 3 hours, for a total of 24 miles.
Then he walks at 3 mph for 8 hours, for a total of 24 miles.

I solved it by trial and error.

Patrick: it all depends on what "in 11 hours" modifies. You're assuming it modifies "walks." I'm assuming it motifies both "bicycles" and "walks." I wonder which of us is right? It is ambiguously worded.
 
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