The speed of a motorboat is to that of the current of water as 36 : 5.

1.	The speed of a motorboat is to that of the current of water as 36 : 5. The boats goes along with the current in 5 hours 10 min. It will come back in (a) 5 hrs 50 min (b) 6 hrs (c) 6 hrs 50 min (d) 12 hrs 10 min
Answer» (c) 6 hrs 50 min Let the speed of the motorboat be 36x km/hr and that of the current of water be 5x km/hr. Speed downstream = (36x + 5x) km/hr = 41x km/hr Speed upstream = (36x – 5x) km/hr = 31x km/hr Time taken to travel downstream = 5 hrs 10 min = \(5\frac{10}{60}\) hrs = \(\frac{31}{6}\) hrs ∴ Distance covered downstream = \(\big(41x\times\frac{31}6\big)\) km ⇒ Distance covered upstream = \(\big(41x\times\frac{31}6\big)\) km ∴ Time taken to travel upstream = \(\big(41x\times\frac{31}6\times\frac1{31x}\big)\) hrs = \(\frac{41}{6}\) hrs = \(6\frac56\) hrs = 6 hrs 50 min.

The speed of a motorboat is to that of the current of water as 36 : 5. The boats goes along with the current in 5 hours 10 min. It will come back in (a) 5 hrs 50 min (b) 6 hrs (c) 6 hrs 50 min (d) 12 hrs 10 min

Answer»

(c) 6 hrs 50 min

Let the speed of the motorboat be 36x km/hr and that of the current of water be 5x km/hr.

Speed downstream = (36x + 5x) km/hr = 41x km/hr

Speed upstream = (36x – 5x) km/hr = 31x km/hr

Time taken to travel downstream = 5 hrs 10 min

= \(5\frac{10}{60}\) hrs = \(\frac{31}{6}\) hrs

∴ Distance covered downstream = \(\big(41x\times\frac{31}6\big)\) km

⇒ Distance covered upstream = \(\big(41x\times\frac{31}6\big)\) km

∴ Time taken to travel upstream = \(\big(41x\times\frac{31}6\times\frac1{31x}\big)\) hrs

= \(\frac{41}{6}\) hrs = \(6\frac56\) hrs = 6 hrs 50 min.

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