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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let t%5B1%5D=walking time and t%5B2%5D=driving time


Now we're going to use the distance-rate-time equation d=rt

Since the walking speed is 4 mph and the walking time is t%5B1%5D, this means r=4 and t=t%5B1%5D

d=4t%5B1%5D Plug in r=4 and t=t%5B1%5D



Also, since the driving speed is 20 mph and the driving time is t%5B2%5D, this means r=20 and t=t%5B2%5D

d=20t%5B2%5D Plug in r=20 and t=t%5B2%5D


Because the distance is the same both ways, this means that d=4t%5B1%5D=20t%5B2%5D


4t%5B1%5D=20t%5B2%5D Start with the given equation


t%5B1%5D=5t%5B2%5D Divide both sides by 4 to isolate t%5B1%5D




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


t%5B1%5D%2Bt%5B2%5D=1.5


5t%5B2%5D%2Bt%5B2%5D=1.5 Plug in t%5B1%5D=5t%5B2%5D


6t%5B2%5D=1.5 Combine like terms


t%5B2%5D=0.25 Divide both sides by 6 to isolate t%5B2%5D


So the driving time is 0.25 hours or 15 minutes

Now let's go back to the equation d=20t%5B2%5D


d=20t%5B2%5D Start with the given equation


d=20%280.25%29 Plug in our answer t%5B2%5D=0.25


d=5 Multiply


So the distance that she traveled is 5 miles