Boat A and Boat B move at a different speeds in still water. If they are to cover a distance of 15 km upstream and then 15 downstream in a river moving at 6 /h the ratio of time taken by A and B is 5:7.what is the speed of boat B, if speed of boat A is 15k km/hr
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Answer:
Given :
Speed of boat in still water =15 km/hr
Let x be speed of the stream in km/hr
Speed of the boat upstream =15−x
Speed of the boat down stream =15+x
Time taken for upstream T
1
=
15−x
30
Time taken for downstream T
2
=
15+x
30
Given, T
1
+T
2
=
2
9
=
15−x
30
+
15+x
30
=
2
9
=30(
15−x
1
+
15+x
1
)=
2
9
=30(
(15−x)(15+x)
15+x÷15−x
)=
2
9
=
225−x
2
30×30
=
2
9
=
225−x
2
100
=
2
1
⇒225−x
2
=200
⇒x
2
=25
⇒x=5 ....(∵x is +ve)
⇒x=5 km/hr
Speed of the stream =5 km/hr.
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