Question

Paul rides his bike from town A to town B. It takes 3 2/3 hours to complete the 20 mile trip from town A to town B. On the slow part of the trip, Paul pedals his bike at a rate of 4 miles per hour. One the fast part of the trip, he pedals at 12 miles per hour. How long does Paul pedal at 4 miles per hour and how long does he pedal at 12 miles per hour?

Answer 1

Start with this, and see if you can get it from there:

\[t=\frac{d}{v} = \frac{d_{slow}}{v_{slow}} + \frac{d_{fast}}{v_{fast}}\]
\[d_{total} = d_{slow} + d_{fast}\]
\[d_{slow} = 20 \text{ miles} - d_{fast}\]
\[t = 3.67 h = \frac{d_{slow}}{4 \text{ mph}} + \frac{d_{fast}}{12 \text{ mph}} = \frac{20 - d_{fast}}{4 \text{ mph}} + \frac{d_{fast}}{12 \text{ mph}}\]

Answer 2

Got it thanks!

Answer 3

No problem.