Q:

It takes Mike 1 hour to get to work each day. He first rides the train, which travels at an average rate of 65 miles per hour. Then he rides the subway train, which travels at an average rate of 25 miles per hour. If the total distance that he travels from home to work is 61 miles, how many minutes does Mike spend riding the subway each morning?

Accepted Solution

A:
Answer:The time taken by Mike riding subway train is 6 min .Step-by-step explanation:Given as :Total time taken by Mike from home to work = t = 1 hoursTotal distance between home and work = 61 milesThe average speed of train = 65 mphLet The distance cover while travelling on train = d milesThe average speed of subway train = 25 mphLet The distance cover while travelling on subway train = (61 - d)  milesLet the time taken by Mike riding subway train = x minNow, From formula∵ Time = [tex]\dfrac{\textrm distance}{\textrm speed}[/tex]So, Total time taken = time taken on train + time taken on subway trainOr, t = [tex]\dfrac{d}{65}[/tex] + [tex]\dfrac{61 - d}{25}[/tex]Or, 1 = [tex]\frac{5 \times d + 13 \times (61 - d)}{325}[/tex]Or, 1 × 325 = 5 d - 13 d + 793Or, 325 = - 8 d + 793Or, 8 d = 468∴    d = [tex]\dfrac{468}{8}[/tex]i.e  d = 58.5So, The distance cover while travelling on subway train = (61 - d) = 61 - 58.5 milesI.e The distance cover while travelling on subway train = 2.5 milesNow, Time taken by Mike on subway train = x =  [tex]\dfrac{\textrm distance}{\textrm speed}[/tex]Or, x =  [tex]\dfrac{2.5}{25}[/tex] hourOr, x = 0.1 hour∵ 1 hour = 60 minutes∴ 0.1 hour = 60 × 0.1 = 6 minutesSo, The  time taken by Mike riding subway train = x = 6 minHence,The time taken by Mike riding subway train is 6 min . Answer