A steamer travelling in a river, moves from P to Q (downstream) in 2.5 hours and from Q to
P (upstream) in 5 hours. If due to monsoon, speed of the river flow gets doubled, find the
new time taken by the same steamer to go from
(a) P to Q (downstream)
(b) Q to P (upstream)
Answers
Answer:
The new time taken by the same steamer to go from
(a) P to Q (downstream) is 2 hours
The new time taken by the same steamer to go from
(b) Q to P (downstream) is 10 hours
Explanation:
Let the speed of the steamer in water is u m/s
and speed of the river be s m/s
Therefore the relative speed for upstream will be : (u-s)
and the relative speed for downstream will be : (u+s)
d(PQ)/u+s= 2.5
d(OP)/u-s= 5
then,
u-s/u+s= 2.5/5
u= 3s
therefore, d(PQ)/4s= 2.5
or, d(PQ)= 10s
due to monsoon, speed of the river flow gets doubled
then the speed of the river is 2s m/s
Therefore,
the new time taken by the same steamer to go from
(a) P to Q (downstream)
t(downstream)= d(PQ)/u+2s
putting the value of u
= d(PQ)/5s
= 10s/5s
= 2 hours
the new time taken by the same steamer to go from
(b) Q to P (downstream)
t(upstream)= d(PQ)/u-2s
= d(PQ)/s
= 10s/s
= 10 hours
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