SOLUTION: Q Alan and Bob walk from school to the library. Alan takes 40 minutes while Bob takes 20 minutes. If they start walking from the school at the same time, how long will it take for

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Question 1088421: Q
Alan and Bob walk from school to the library. Alan takes 40 minutes while Bob takes 20 minutes. If they start walking from the school at the same time, how long will it take for Bob to be 2/5 as far as Alan from the library?
Can you help solve this? I'm not quite sure how to deal with the 2/5 fraction.
Thanks in advance.
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!
.
The Alan's rate is D%2F40 of the distance D to the library per minute.

The Bob's rate is D%2F20 of the distance D to the library per minute.


During t minutes Alan will cover the distance  t%2A%28D%2F40%29, and will be at the distance D-t%2A%28D%2F40%29 from the library.

          while  Bob  will cover the distance  t%2A%28D%2F20%29, and will be at the distance D-t%2A%28D%2F20%29 from the library.


They ask you: find t in the way that

D-t%2A%28D%2F20%29 = %282%2F5%29%2A%28D-t%2A%28D%2F40%29%29.


Cancel D in both sides and multiply both sides by 5. You will get

5%2A%281-t%2F20%29 = 2%2A%281-t%2F40%29.


Now multiply by 40 both sides. You will get

5*(40-2t) = 2*(40-t)  ====>  200 - 10t = 80 - 2t  ====>  200 - 80 = 10t - 2t  ====>  8t = 120  ====>  t = 15 minutes.


It is your 

Answer.  The time under the question is 15 minutes.

Solved.