Question 1196154
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15 min = 15/60 = 0.25 hour


x = amount of time, in hours, the mother has been driving
x+0.25 = amount of time, in hours, Rick is on his bike
Rick got a 0.25 hour head start so he's been on the road for that much longer


distance = rate*time
We'll use that to figure out the equations for Rick and his mother.


Rick:
d = r*t
d = 10*(x+0.25)
d = 10*x+10*0.25
d = 10*x+2.5


His mother:
d = r*t
d = 40x


It might be handy to have a table like this<table border = "1" cellpadding = "5"><tr><td></td><td>Distance (miles)</td><td>Rate (mph)</td><td>Time (hrs)</td></tr><tr><td>Rick</td><td>10x+2.5</td><td>10</td><td>x+0.25</td></tr><tr><td>Mother</td><td>40x</td><td>40</td><td>x</td></tr></table>In order for his mother to catch up to him, their distances must be the same.
40x = 10x+2.5	
40x - 10x = 2.5	
30x = 2.5
x = 2.5/30	
x = 25/300
x = (1*25)/(12*25)
x = 1/12
It takes the mother 1/12 of an hour to catch up to her son.


1/12 of an hour = (1/12)*60 = 60/12 = 5 minutes	which is a more feasible time unit to work with.


Answer: <font color=red>5 minutes</font> (i.e. 1/12 of an hour)
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