Question

A boat goes 16km upstream and 24km downstream in 6hrs. It can go 12km up and 36km down in the same time. Find the speed of the boat in still water and the speed of the stream.

Answer 1

Answer:

8,4

Step-by-step explanation:

16/(x-y) + (24/x+y) = 6 & 12/(x- y) + 36/(x+y) = 6

let's assume 1/(x -y) = u , 1/(x+ y) = v

16u + 24v = 6 , 12u + 36v = 6

multiply (1) by 3 & (2) by 4 or subtract (2) from (1)

72v = 6 => v = 1/12 & u = 1/4

x-y = 4, x + y = 12 => 2x = 16 => x = 8 km/hr ( in still water ) & y = 4 km/hr (stream)

Answer 2

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Let the speed of the boat in still water be x km/h.

speed of the stream be y km/h.

Now,

Speed of upstream = (x - y) km/h.

speed of Downstream = (x + y) km/h.

Then,

Time taken to cover 16 km upstream = 16/(x-y) h.

Time taken to cover 24 km downstream = 24/(x+y) h.

Total time taken = 6 hours.

∴ $\rm\:\dfrac{16}{(x-y)}+\dfrac{24}{(x+y)}=6\:......(i)$

again,

Time taken to cover 12 km upstream = 12/(x-y) h.

Time taken to cover 36 km downstream = 36/(x+y) h

Total time taken = 6 hours.

∴ $\rm\:\dfrac{12}{(x-y)}+\dfrac{36}{(x+y)}=6\:......(ii)$

Putting 1/(x-y) = a and 1/(x+y) = b in eq (i) and (ii)

$\rm\:16a+24b=6$

$\rm\:8a+12b=3\:................(iii)$

then,

$\rm\:12a+36b=6$

$\rm\:2a+6b=1\:.................(iv)$

on multiplying eq (iv) by 4 and subtracting eq(iii) from it,we get.

$\rm\:12b=1$

$\rm\implies\:b=\dfrac{1}{12}$

$\rm\implies\:\dfrac{1}{(x+y)}=\dfrac{1}{12}$

$\rm\implies\:x+y=12\:...............(v)$

On multiplying eq (iv) by 2 and subtracting it from eq (iii) we get,

$\rm\:4a=1$

$\rm\implies\:a=\dfrac{1}{4}$

$\rm\implies\:\dfrac{1}{(x-y)}=\dfrac{1}{4}$

$\rm\implies\:x-y=4\:...............(vi)$

on adding eq (v) and (vi),we get

$\rm\:2x=16$

$\rm\implies\:x=\cancel\dfrac{16}{2}$

$\rm\implies\:x=8$

on subtracting eq(vi) from eq(v),we get

$\rm\:2y=8$

$\rm\implies\:y=\cancel\dfrac{8}{2}$

$\rm\implies\:y=4$

Hence,Speed of boat in still water will be 8 km/h

and speed of stream will be 4 km/h.