A girl walked from her home into town at the rate of 4 miles

A girl walked from her home into town at the rate of 4 miles per hour. She returned by bus over the same route. The bus averaged 20 miles per hour, and the entire round trip took 1 hour and 40 minutes, including the 10 minute wait for the bus. How far did the girl walk?

Solution

Let =walking time and =driving time


Now we\'re going to use the distance-rate-time equation

Since the walking speed is 4 mph and the walking time is , this means and

Plug in and



Also, since the driving speed is 20 mph and the driving time is , this means and

Plug in and


Because the distance is the same both ways, this means that


Start with the given equation


Divide both sides by 4 to isolate




If the entire trip took 1 hour and 40 minutes and there was a 10 minute wait, then the traveling portion took 1 hour and 30 minutes (which is 1.5 hours)


So the sum of these two times is 1.5. In other words, we have this first equation





Plug in


Combine like terms


Divide both sides by 6 to isolate


So the driving time is 0.25 hours or 15 minutes

Now let\'s go back to the equation


Start with the given equation


Plug in our answer


Multiply


So the distance that she traveled is 5 miles