A boat covers a certain distance downstream in 5 hours but takes 7 hours to return upstream to the starting point. If the speed of the stream is 3 km/h, then find the speed of the boat.

Speed of the boat = z(x + y)/(x - y)

Where, z = Speed of the stream,

x = Time taken in upstream,

y = Time taken in downstream

Here, x = 7, y = 5  and z = 3

Speed of the boat = 3(7 + 5)/(7 - 5)

⇒ 3(12/2)

⇒ 3 × 6

⇒ 18 km/h

∴ The speed of the boat will be 18 km/h.

Traditional method:

Given:

Speed of the stream = 3 km/h

Time taken in upstream = 7 hours

Time taken in downstream = 5 hours

Formula Used:

Upstream speed = (Speed of the boat) - (Speed of the stream)

Downstream speed = (Speed of the boat) + (Speed of the stream)

Distance = Time × Speed

Calculation:

Let the speed of the boat be x km/h and distance be d km.

Upstream speed = (x - 3) km/h

Downstream speed = (x + 3) km/h

According to the question,

(x - 3) = (d/7)

⇒ x = 3 + (d/7) ......(1)

And, (x + 3) = (d/5)

Now, from equation (1),

3 + (d/7) + 3 = d/5

⇒ 6 = (d/5) - (d/7)

⇒ 6 = {(2d)/35}

⇒ 2d = 6 × 35

⇒ d = 3 × 35

⇒ d = 105 km

Again, from equation (1),

x = 3 + (105/7)

⇒ x = 3 + 15

⇒ x = 18

∴ The speed of the boat will be 18 km/h.