Question

A woman can bicycle 27 miles in the same time it takes her to walk 9 miles. she can ride 10 mph faster than she can walk. how fast can she walk

Answer 1

Let the time be t. We don't necessarily need to find the elapsed time, but do need to find her usual walking speed.

Recall that distance = (rate)(time)

Walking speed = s

driving speed = s + 10 (mph)

27 mi 9 mi
Then t = ----------------- = ------------
(s+10) mph s mp

This equation has only one variable, s. We can solve it for s as follows:

( 27 mi) * (s ) = (9 mi)(s)+ 90 (mi)(mph)

27s = 9s + 90, or 18 s = 90, or s = 90/18 = 10/2 = 5. Her walking speed is 5 mph. Her riding speed is 5+10 mph, or 15 mph.

Both 5 mph and 15 mph sound reasonable, don't they? 5 mph on foot and 15 on the bike.