SOLUTION: John leaves for work at 8:30 a.m. every day. If he drives 30 mph, he is 5 minutes later than his target arrival time. If he drives 50 mph, he is 5 minutes earlier than this target

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Question 281422: John leaves for work at 8:30 a.m. every day. If he drives 30 mph, he is 5 minutes later than his target arrival time. If he drives 50 mph, he is 5 minutes earlier than this target arrival time. The speed at which he should drive to hit his target arrival time exactly is:
(A)35 mph (B) 37.5 mph (C) 40 mph (D) 42.5 mph (E) 45 mph

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Let the time required to reach the exact time be t
If he drives at 30 mph he reaches 5 minutes late that is t+1/12 hours
If he drives at 50 mph then he takes t-1/12 hours
the distance traveled is the same
30(t+1/12) =50(t-1/12)
30(12t+1)/12 = 50(12t-1)/12
360t+30=600t-50
240t=80
t=1/3 hour
When speed is 30 mph the time taken = 1/3 +1/12 hours = 5/12 hours
When time taken is 1/3 what will be the speed. ( Inverse proportion)
5/12* 30 / 1/3
5/12*30 *3/1
=37.5 mph