Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • If a motor boat can travel 30 km upstream and 28 downstream in 7h it can travel 21 km upstream and return in 5h find the speed of boat in still water

If a motor boat can travel 30 km upstream and 28 downstream in 7h it can travel 21 km upstream and return in 5h find the speed of boat in still water

Answers (1)

best_answer

Let the speed of the boat in still water be x km/h and speed of the stream is y km/h.

Therefore, speed of the boat while upstream is (x−y) km/h and speed of the boat while downstream is (x+y) km/h

\text {time}=\frac{\text {distance}}{\text {speed}}

 

\frac{30}{x+y}+\frac{28}{x-y}=7 \quad \ldots \ldots \ldots \ldots (1)$ \\ $\frac{21}{x+y}+\frac{21}{x-y}=5 \quad \ldots \ldots \ldots \ldots .(2)$ \\ Let $\frac{1}{x+y}=u$ and $\frac{1}{x-y}=v,$ then the equations (1) and (2) becomes: \\ $30 u+28 v=7 \ldots \ldots \ldots(3)$ \\ $21 u+21 v=5 \ldots \ldots \ldots(4)$ \\ Multiplying equation (3) by 21 and equation (4) by 30 we get, \\ $630 u+588 v=147 \ldots \ldots \ldots$ \\ $630 u+630 v=150 \ldots \ldots \ldots .(6)$ \\ Now subtracting equation (5) from equation (6), we get

42 v=3$ \\ $\Rightarrow v=\frac{1}{14}$ \\Substitute the value of $v$ in equation (4) then, $u=\frac{1}{6}$ \\since $\frac{1}{x+y}=u$ and $\frac{1}{x-y}=v,$ therefore, \\$x+y=6 \ldots \ldots \ldots .(7)$ \\$x-y=14 \ldots \ldots \ldots .(8)$ \\Adding equations (7) and (8) , we get: \\$2 x=20$ \\$\Rightarrow x=10$ \\Hence, the speed of the boat in still water is $10 km / h$.

Posted by

Deependra Verma

View full answer

Similar Questions

Latest Question