SOLUTION: A takes 30 minutes to reach a shop from his residence. B takes 20 minutes to reach the same shop from same residence. one day A departed to shop at 8a.m. if B departed 5 minutes l

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Question 1065487: A takes 30 minutes to reach a shop from his residence. B takes 20 minutes to reach the same shop from same residence. one day A departed to shop at 8a.m. if B departed 5 minutes later. at what time B passes A?
Answer by ikleyn(52797) About Me  (Show Source):
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A takes 30 minutes to reach a shop from his residence. B takes 20 minutes to reach the same shop from same residence.
one day A departed to shop at 8a.m. if B departed 5 minutes later. at what time B passes A?
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Let D be the distance from the residence to the shop.

A has the speed D%2F30 units per minute, while B has the speed D%2F20 units per minute.

Let "t" be the time counted from 8:05 am.

The distance for B is t%2A%28D%2F20%29.

The distance for A is 5%2A%28D%2F30%29+%2B+t%2A%28D%2F30%29.

The equation for the time is

t%2A%28D%2F20%29 = 5%2A%28D%2F30%29+%2B+t%2A%28D%2F30%29.

Multiply everything by 60/D. You will get

3t = 5*2 + 2t,   or

3t - 2t = 10,

t = 10. 

Answer.  B passes A at 8:15 am.

Solved.