Question

5.
A steamer travelling in a river, moves from P to Q (downstream) in 2.5 hours and from Oto P
(upstream) in 5 hours. If due to monsoon, speed of the river flow gets doubled, find the new tim
taken by the same steamer to go from
(a) P to Q (downstream)
(b) Q to P(upstream)​

Answer 1

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