The Alan's rate is  of the distance D to the library per minute.

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


During t minutes Alan will cover the distance  , and will be at the distance  from the library.

          while  Bob  will cover the distance  , and will be at the distance  from the library.


They ask you: find t in the way that

 = .


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

 = .


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.