Question

a boat travels 16 km upstream and 24 km downstream in 6 hours the same boat travels 36 km upstream and 48 km downstream in 13 hours find the speed of the water current and speed of boat in still water

Answer 1

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Answer 2

Answer:

speed of the boat upstream = 4 km/hr

Speed of the boat downstream = 12 km/hr

Step-by-step explanation:

Let the speed of the boat in still water be B

Let the Speed of the boat in the stream  be S.

Downstream speed = (B+S) km/hr

Upstream speed = (B-S) km/hr

Now we are give that

a boat travels 16 km upstream and 24 km downstream in 6 hours the same boat travels 36 km upstream and 48 km downstream in 13 hours

Now $Time = \frac{Distance}{Speed}$

So, $\frac{24}{B+S} +\frac{16}{B-S} = 6$  --1

$\frac{48}{B+S} +\frac{36}{B-S} = 13$   --2

Now solve both equations:

Putting $\frac{1}{B+S} =u$

Putting $\frac{1}{B-S} =v$

So, equation becomes:

$24u+16v = 6$   ---3

$48u+36v = 13$  --4

Now solve these equation using substitution method

Substitute the value of u from 3 in 4

$48(\frac{6-16v}{24})+36v = 13$

$2(6-16v)+36v = 13$

$12-32v+36v = 13$

$12+4v = 13$

$4v=1$

$v=\frac{1}{4}$

Now substitute the value of v in 3 to get value of u

$24u+16(\frac{1}{4})= 6$

$24u+4 = 6$

$24u=2$

$u=\frac{2}{24}$

$u=\frac{1}{12}$

So,$\frac{1}{B+S} =\frac{1}{12}$   --5

,$\frac{1}{B-S} =\frac{1}{6}$  --6

Solving 5 and 6 we get

B = 4 km/hr

S = 12km/hr

Thus, speed of the boat upstream = 4 km/hr

Speed of the boat downstream = 12 km/hr