Anika ran from her house to the library at an average speed of 10 kmph and returned along the same route at an average speed of 15 kmph. If it took her 20 minutes in total to run to the library and come back, how many minutes did it take to run from her house to the library?

Question: Anika ran from her house to the library at an average speed of 10 kmph and returned along the same route at an average speed of 15 kmph. If it took her 20 minutes in total to run to the library and come back, how many minutes did it take to run from her house to the library?

Solution:
Let the distance be d km.
Time taken to go = d/10 hour, Time taken to return = d/15 hour.
Total time = 20 min = 1/3 hour.

According to the question,
(d/10) + (d/15) = 1/3
⇒ (3d + 2d)/30 = 1/3
⇒ 5d/30 = 1/3
⇒ d/6 = 1/3
⇒ d = 2 km.

∴ Time to go to library = (d/10) hour = 2/10 = 1/5 hour.
In minutes = (1/5) × 60 = 12 minutes.