A woman can bicycle 25 miles in the same time as it takes her to walk 5 miles she can ride 10 mph faster than she can walk how fast can she walk?

The woman walks at 2.5 mph.

Bonus: she rides her bicycle at 12.5 mph.

Step-by-step explanation:

We're told that she can bicycle 25 miles in the time takes her to walk 5.  That means that on a bicycle, she moves 25 ÷ 5, or 5 times faster on a bicycle than when she runs.

We're also told that she can ride at 10 mph faster than she can walk.

That gives us two relationships to describe.  If we call her speed on the bicycle "b", and her speed on foot "w", then we know:

b = 5w

and

b = w + 10

Since both of those describe b, we can simply equate them.  Stating the obvious:

b = b

therefore:

5w = w + 10

We can then simplify:

5w = w + 10

4w = 10

w = 2.5

So she walks at 2.5 miles per hour.

We can test that answer too.  Let's compare to the first statement, her bicycling 25 miles in the time it takes to walk five miles.

Walking 2.5 miles per hour means she'd take two hours to walk five miles.

We also know that she can ride 10mph faster, so she rides at 12.5 mph.  two times that is 25, so she would indeed cover 25 miles on her bicycle in the same time that she walks five.

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