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.

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

and speed of the stream = y km/hr

Then, the speed of the boat downstream = (x + y)km/hr

And speed of the boat upstream = (x – y)km/hr

According to the question

Condition I: When boat goes 16 km upstream, let the time taken be t₁.

Then,

When boat goes 24 km downstream, let the time taken be t₂.

Then,

But total time taken (t₁ + t₂) = 6 hours

…(a)

Condition II: When boat goes 12 km upstream, let the time taken be T₁.

Then,

When boat goes 36 km downstream, let the time taken be T₂.

Then,

But total time taken (T₁ + T₂) = 6 hours

…(b)

Now, we solve tis pair of linear equations by elimination method

…(i)

And …(ii)

On multiplying Eq. (i) by 3 and Eq. (ii) by 4 to make the coefficients equal of first term, we get the equation as

…(iii)

…(iv)

On substracting Eq. (iii) from Eq. (iv), we get

⇒ x – y = 12 …(a)

On putting the value of x – y = 12 in Eq. (i), we get

⇒ x + y = 4 …(b)

Adding Eq. (a) and (b), we get

⇒ 2x = 16

⇒ x = 8

On putting value of x = 8 in eq. (a), we get

8 – y = 12

⇒ y = – 4 but speed can’t be negative

⇒ y = 4

Hence, x = 8 and y = 4 , which is the required solution.

Hence, the speed of the boat in still water is 8km/hr and speed of the stream is 4km/hr