SOLUTION: 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

Question 124676: 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?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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

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