Question

A boat goes 16 km upstream and 24 km downstream in 6 hours.
Also, it covers 12 km upstream and 36 km downstream in the
same time. Find the speed of the boat in still water and that of
the stream​

Answer 1

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

and the speed of the stream be y km/hr.

Then, speed upstream = (x−y)km/hr

and speed downstream = (x+y)km/hr

Time taken to cover 16 km upstream = 16(x−y) hours

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

Total time taken = 6 hours.

∴16x−y+24x+y=6 .........(i)

Again, time taken to cover 12 km upstream = 12(x−y) hours.

Time taken to cover 36 km downstream = 36(x+y) hours.

∴12x−y+36x+y=6........(ii)

Putting 1(x−y) = u and 1(x+y)=v in (i) and (ii),

we get

16u+24v=6 ⇒8u+12v=3... (iii)

12u+36v=6 ⇒ 2u+6v=1.... (iv)

On multiplying (iv) by 4 and subtracting (iii) from the result,

we get

12v = 1⇒v = 112

⇒1x+y = 112

112⇒x+y = 12.......(v)

On multiplying (iv) by 2 and subtracting the result from (iii),

we get

4u = 1⇒u = 14

14⇒1x−y = 14⇒x−y = 4...(vi)

On adding (v) and (vi),

we get

2x = 16⇒x = 8.

On subtracting (vi) from (v),

we get

2y = 8⇒y = 4.

________________________

OM!

Answer 2

Step-by-step explanation:

Explanation:

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

Let the speed of the current be y km/hr.

The speed of the boat downstream = x + y

The speed of the boat upstream = x - y

Given that the boat goes 16km upstream and 24 km downstream in 6 hours.

= > (16/x - y) + (24/x + y) = 6   ------- (1)

Given that it covers 12km upstream and 36km downstream in same time. 

= > (12/x - y) + (36/x + y) = 6  -------- (2)

On solving (1) * 3 & (2) * 4, we get

Let 1/x - y = u, 1/x + y = v

Now,

48u + 72v = 18

48u + 144v = 24

---------------------------

           -72v = -6

                v = 1/12

Substitute v = 12, we get

48u + 72v = 18

48u + 72(1/12) = 18

48u + 6 = 18

48u = 18 - 6

48u = 12

u = 12/48

u = 1/4.

Hence, u = 1/4

 => 1/x - y = (1/4)

=> x - y = 4.

Hence, v = 1/12.

=> 1/x + y = 1/12

=> x + y = 12.

Verification:

Let us take x = 8, y = 4.

=> 8 +  4 = 12

=> 8 - 4 = 4.

Therefore Speed of the boat in still water = 8 km/hr.