Question
Download Solution PDFThe ratio of the speed of a motorboat to that of the current of water is 31 ∶ 6. The motorboat starts from a point and covers a certain distance along the current in 4 h 10 min. Find the time taken by the motorboat to come back to its initial point.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
Total time = 4 hr 10 min.
The ratio of the speed of a motorboat to that of the current of water is 31 ∶ 6.
Formula used
Speed = Distance/Time
Detailed solution:-
Let the common factor of speeds of a motorboat to that of the current of water be x.
Then, the speed of the motorboat = 31x km/h,
The speed of the current = 6x km/h.
Motorboat goes along with the current in 4 h 10 m = 4 h +10/ 60 h = 25/6 h
Speed of downstream = 31x + 6x = 37x km/h
Speed of upstream = 31x – 6x = 25x km/h
Now, the distance covered by the downstream
⇒ speed of downstream × Time taken = 37x × (25 /6) km
Similarly, the distance covered upstream is also 37x × (25 /6)km
Time is taken by upstream = Distance covered by upstream/ Speed of upstream
⇒ [37x × (25 /6) ]/25x
⇒ 37/ 6 = 6h + 1/ 6 = 6h 10 min
∴ The time the motorboat requires to return is equal to 6 hours 10 minutes.
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