SOLUTION: A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to o

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to o      Log On


   

Question 685085: A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to overtake the boy in 15 minutes?
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to overtake the boy in 15 minutes?
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Boy DATA:
rate = 8 mph ; time = 5/4 hrs. ; distance = 8(5/4) = 10 miles
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Father DATA:
time = 1/4 hrs ; distance = 10 miles ; rate = d/t = 10/(1/4) = 40 mph
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Cheers,
Stan H.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A boy leaves on a bicycle trip at the rate of 8 mph. One hour later the father, realizing that his son forgot his camping gear, sets out by car. How fast must the father drive to overtake the boy in 15 minutes? 
Suppose the father has to travel at x mph.  One hour later the son is 
8 miles up the road.  The father's approach rate is x-8 mph.  15 minutes
converted to hours is 1%2F4 hour.  Since DISTANCE = RATE×TIME,

             8 = (x-8)1%2F4

Multiply both sides by 4
    
            32 = x - 8
            40 = x

The father must drive 40 mph.

Edwin