Question

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)

Answer 1

Answer:

(a)1.25 hrs

(b)2.5 hrs

Answer 2

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