Ben was walking in Manhattan at a constant speed. He went along 5th avenue from 4th to 98th street. At 3:00 he was on 15th street, and at 4:30 he was on 45th street. When did he start and when did he finish his walk?

Write an equation which could tell on what street N he was T minutes after he started to walk.

1 Answer
Feb 28, 2018

Ben started at 2:27 (14:27) and finished at 7:09 (19:09).


Ben was walking at a constant speed, and we know it took him #1 1/2# hours to go the 30 blocks between 15th and 45th streets. #1 1/2# hours = 90 minutes and #90 -: 30 = 3#, so he was walking at a pace of 3 minutes per block. He started at 4th Street, which is 11 blocks before 15th Street. #11 * 3 = 33#, so we subtract 33 minutes from 3:00 to determine the start time of 2:27. The distance between 45th Street and 98th Street is 53 blocks. #53*3 = 159#. 159 minutes is 2 hours and 39 minutes. If we add that to the time of 4:30 (which is when he reached 45th Street), we get 7:09 as his finish time.