How fast can she walk?

Question

A woman can bicycle 20 miles in the same time as it takes her to walk 6 miles. She can ride 7 mph faster than she can walk. 

Answer 1

Distance equals velocity times time (d=vt).

 

Let vb=velocity biking.

Let vw=velocity walking.

 

Since the times for walking and biking are the same, d/vb = d/vw.

 

20/vb = 6/vw

 

Also, vb = vw +7 (she can ride 7 mph faster than walking)

 

Two equations, two unknowns - Using substitution method:

 

20/(vw+7) = 6/vw

 

Cross-multiply:

 

20vw = 6(vw+7)

 

20vw = 6vw + 42

 

14vw = 42

 

vw = 3

 

Thus, she walks at 3 mph, and she rides at 10 mph.