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?

<pre>
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 {{{1/4}}} hour.  Since DISTANCE = RATE×TIME,

             8 = (x-8){{{1/4}}}

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

The father must drive 40 mph.

Edwin</pre>