Question

A boat goes $12km$ upstream and $40km$ downstream in $8$hrs. It can go $16km$ downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

• A. Speed of boat in still water $=9km/hr$ and speed of stream $6km/hr$.
• B. Speed of boat in still water $=6km/hr$ and speed of stream $2km/hr$.
• C. Speed of boat in still water $=14km/hr$ and speed of stream $32km/hr$.
• D. Speed of boat in still water $=7km/hr$ and speed of stream $23km/hr$.

Answer 1

Answer: (B)

Speed of boat in still water $=6km/hr$ and speed of stream $2km/hr$.

Let

Speed of the boat in still water be xkm/hr

Speed of the stream be ykm/hr

Speed of boat in downstream $=$ (x+y)km/hr

Speed of boat in upstream $=$ xy)km/hr

According to given problem

Time taken to cover 12km upstream $=\frac{12}{x-y}hrs$

Time taken to cover 40km downstream $=\frac{40}{x+y}hrs$

But, the total time taken $=$8hr

$=\frac{12}{x-y}+\frac{40}{x+y}hrs=8$.........(1)

Time taken to cover 16km upstream $=\frac{16}{x-y}$ hrs

Time taken to cover 32km downstream $=\frac{32}{x+y}$hrs

Total time taken $=$ 8hr

$=\frac{16}{x-y}+\frac{32}{x+y}hrs=8$.......(2)

$Put\frac{1}{x-y}=pand\frac{1}{x+y}=q$

hence we get equation

12p + 40q $=$ 8....(3)

16p + 32q $=$ 8....(4)

Furthur simplyfying the eq we get

3p + 10q $=$ 2..........(3)

2p + 4q $=$ 1.........(4)

Multiply eq (3) by 2 and eq (4) by 3

6p + 20q $=$ 4...........(3)

6p + 12q $=$ 3............(4)

subtracting eq (4) from eq(3) we get

$q=\frac{1}{8}$

and we get $p=\frac{1}{4}$

$Hencep=\frac{1}{x-y}=\frac{1}{4}andq=\frac{1}{x+y}=\frac{1}{8}$

x-y $=$ 4..(5)

x+y$=$ 8....(6)

Solving equation(5) and (6) we get x $=$ 6 and y$=$2

Hence speed of boat in still water =6km/hr and speed of stream 2km/hr.