Expert: Scott A Wilson - 2/15/2010

Question
A motorcycle breaks down and the rider has to walk the rest of the way to work.  The bike was traveling at 45 mi/h and the rider walks at 6 mi/h.  The distance from home to work is 25 miles, and the total time was 2 hours.  How far did the motorcycle go before it broke down?

Answer
The total time was 2 hours, so he road t hours and walked for 2-t hours.
The total distance equation is then 45t + 6(2-t) = 25.
Multiplying gives 45t + 12 - 6t = 25.

Simplifying and subtracting 12 from both sides gives 39t = 13.
Division of both sides by 39 gives t = 1/3 hours.

Since 1 hour = 60 minutes, thats 20 minutes.

To try this out, put 1/3 back in the original equation.
This gives 45/3 + 6(2 - 1/3) = 15 + 6(5/3) = 15 + 30/3 = 15 + 10 = 25.

This gave us the answer and checked the value at the same time.
The answer would be 15 miles.