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 hours
Total distance between home and work = 61 miles
The average speed of train = 65 mph
Let The distance cover while travelling on train = d miles
The average speed of subway train = 25 mph
Let The distance cover while travelling on subway train = (61 - d) miles
Let the time taken by Mike riding subway train = x min
<u>Now, From formula</u>
∵ Time = ![\dfrac{\textrm distance}{\textrm speed}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20distance%7D%7B%5Ctextrm%20speed%7D)
So, Total time taken = time taken on train + time taken on subway train
Or, t =
+ ![\dfrac{61 - d}{25}](https://tex.z-dn.net/?f=%5Cdfrac%7B61%20-%20d%7D%7B25%7D)
Or, 1 = ![\frac{5 \times d + 13 \times (61 - d)}{325}](https://tex.z-dn.net/?f=%5Cfrac%7B5%20%5Ctimes%20d%20%2B%2013%20%5Ctimes%20%2861%20-%20d%29%7D%7B325%7D)
Or, 1 × 325 = 5 d - 13 d + 793
Or, 325 = - 8 d + 793
Or, 8 d = 468
∴ d = ![\dfrac{468}{8}](https://tex.z-dn.net/?f=%5Cdfrac%7B468%7D%7B8%7D)
i.e d = 58.5
So, The distance cover while travelling on subway train = (61 - d) = 61 - 58.5 miles
I.e The distance cover while travelling on subway train = 2.5 miles
Now, Time taken by Mike on subway train = x = ![\dfrac{\textrm distance}{\textrm speed}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20distance%7D%7B%5Ctextrm%20speed%7D)
Or, x =
hour
Or, x = 0.1 hour
∵ 1 hour = 60 minutes
∴ 0.1 hour = 60 × 0.1 = 6 minutes
So, The time taken by Mike riding subway train = x = 6 min
Hence,The time taken by Mike riding subway train is 6 min . Answer