A motorboat can travel at 10 km/hr in still water. It travelled 91 km downstream and then returned, taking 20 hours altogether. Help to calculate the speed of flow of water in the river. - Find 6 Answers & Solutions

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Question: A motorboat can travel at 10 km/hr in still water. It travelled 91 km downstream and then returned, taking 20 hours altogether. Help to calculate the speed of flow of water in the river.

Posted by: Praddep on: 16 Aug, 2017

6 Answers by Expert Tutors

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Answer

let the speed of stream be u. speed downstream would be (10+u)km/hr and upstream would be (10-u)km/hr. Time to cover 91 km downstream would be 91/(10+u) hrs and Time to cover 91 km upstream would be 91/(10-u) hrs Total time would be 91/(10+u) + 91/(10-u) = 20 hrs (given) => (91(10-u) + 91(10+u))/(100-u^2) = 20 => 1820 = 20(100-u^2) =>91 = 100 - u^2 =>u^2 = 9 => u=3km/hr. (which is the required speed of flow of water).

Answer by:

Anurag Agarwal, Faridabad

Answer

20= 91/(10+v) + 91/(10-v) 20= 910*2 / (100-v^2) 100-v^2 = 91 v^2= 9 v= 3km/hr

Answer by:

Upinderjeet Singh, Delhi

Answer

upstream= 10-3=7 downstream=10+3=13 91 is divisible by both.. now check it.. 91/13=7 91/7=13 7+13=20 hours.

Answer by:

Anonymous

Answer

let v be the speed of water then for downstream speed of boat will be (10-v) for 91km distance and for upstream it will be (10-v) for again 91km distance to reach at starting point. total time taken will be 20 hr so equating as time equation as (91/(10+v))+(91/(10-v))=20. By calculating v, we get v=3km/hr

Answer by:

Brijgopal Suthar, Bangalore

Answer

if options are given..then its a mind work.. suppose speed of water is 3. so upstream= 10-3=7 downstream=10+3=13 91 is divisible by both.. now check it.. 91/13=7 91/7=13 7+13=20 hours...satisfied

Answer by:

Arpita Kundu, Kolkata

Answer

Let the speed of flow of water = v ; Now, in downstream flow, the net speed of motorboat=(10+v) ; And during return, the boat is flowing against the flow of water, so it's net speed=(10-v) ; Now, time taken for flowing 91km downstream= (Distance)/(net flow speed)= (91)/(10+v) ; And .time taken for flowing 91km upstream(return)= (Distance)/(net flow speed)= (91)/(10-v) ; Now, total time of flow=20 hours ; So, { [ (91)/(10+v) ] + [ (91)/(10-v) ] }=20 ; => [ (1820)/(10^2-v^2) ] = 20 ; => (10^2-v^2)=91 => v=3 km/h ; So the speed of flow of water=3 km/h

Answer by:

Praveen Kumar, Varanasi

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