SOLUTION: Ben drove to Kate’s house. It took 30 mins. On the trip back to her own house, Ben drove an average of 15 mph slower than the trip to Kate’s house and it took an extra 15 mins. How

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Question 1101314: Ben drove to Kate’s house. It took 30 mins. On the trip back to her own house, Ben drove an average of 15 mph slower than the trip to Kate’s house and it took an extra 15 mins. How far is it from Ben’s house to Kate’s house?
Answer by ikleyn(52795) About Me  (Show Source):
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Ben drove to Kate’s house. It took 30 mins. On the trip back to her own house, Ben drove an average of 15 mph slower
than the trip to Kate’s house and it took an extra 15 mins. How far is it from Ben’s house to Kate’s house?
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Is Ben  "he"  or  "she" ?


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Comment from student: Sorry, Ben is a he.
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My response: OK. 

The way to Katy took 30 minutes = 1%2F2 of an hour.

The way back took 45 minutes = 3%2F4 of an hour.


The "distance equation", saying that both ways distance is the same is

%281%2F2%29%2Av = %283%2F4%29%2A%28v-15%29,   where "v" is the average speed on the way "to there".


Multiply both sides by 4. You will get

2v = 3*(v-15)  ====>

2v = 3v - 45  ====>  v = 45.


Then one way distance is %281%2F2%29%2Av = %281%2F2%29%2A45 = 22.5 miles.


Check.  The way "to there" 225%2F45 = 1%2F2 of an hour.

        The way back  22.5%2F%2845-15%29 = 22.5%2F30 = 3%2F4 of an hour.  ! Correct !


Answer.  One way distance is 22.5 miles.