Two boats A and B move away from a buoy anchored at the middle of a river along mutually perpendicular straight lines. The boat A moves along the stream and the boat B across the river. After moving off an equal distance from the buoy, both the boats returned to their original position. Calculate the ratio of the times taken by boat A to that taken by boat B if the velocity of each boat with respect to still water is 2 times the stream velocity.
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Answer:
Let l be the distance covered by the boat A along the river as well as by the boat B across the river. Let v
0
be the stream velocity and v
′
the velocity of each boat with respect water. Therefore time taken by the boat A in its journey
t
A
=
v
′
+v
0
l
+
v
′
−v
0
l
and for the boat B t
B
=
v
′
2
−v
0
2
l
+
v
′
2
−v
0
2
l
=
v
′
2
−v
0
2
2l
Hence,
t
B
t
A
=
v
′
2
−v
0
2
v
′
=
η
2
−1
η
(whereη=
v
v
′
)
On substitution
t
B
t
A
=1.8
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