Question

A motor boat can travel 30 kin upstream and 28 km downstream in 7 hours. It cantravel 21 km upstream and
return in 5 hours. Find the speed of the boat in still water andthe
speed of the stream
​

Answer 1

Given:-

• A motor boat can travel 30 kin upstream and 28 km downstream in 7 hours.
• It can travel 21 km upstream and return in 5 hours.

To find:-

• The speed of the boat in still water and the speed of the stream.

Solution:-

Let,

• the speed of the boat in still water be xkm/hr.
• the speed of the stream be ykm/hr.

Here,

• Speed upstream = x - y.
• Speed Downstream = x + y.

According to the question,

→ 30/x - y + 28/x + y = 7

Let,

• 1/x - y = a
• 1/x + y = b

→ 30a + 28b = 7 ---------- (1).

Then,

→ 21/x - y + 21/x + y = 5

Let,

• 1/x - y = a
• 1/x + y = b

→ 21a + 21b = 5 ---------- (2).

After solving (1) × 21 & (2) × 28

We get,

→ 630a + 588b = 147

→ 588a + 588b = 140

→ 42a = 7

→ a = 1/6.

• Substitute a = 6 in (1)

→ 30a + 28b = 7

→ 30(1/6) + 28b = 7

→ 5 + 28b = 7

→ 28b = 7 - 5

→ 28b =2

→ b = 2/28

b = 1/14.

We know that,

→ a = 1/x - y

→ 1/6 = 1/x - y

→ x - y = 6 ---------- (3).

We know that,

→ b = 1/x + y

→ 1/14 = 1/x + y

→ x + y = 14 --------- (4).

After solving (3) & (4)

We get,

→ x + y = 14

→ x - y = 6

→ 2x = 20

→ x = 10

• Substitute x = 10 in (4)

→ x + y = 14

→ 10 + y = 14

→y = 14 - 10

→ y = 4

Hence,

• the speed of the boat in still water is 10km/hr.
• the speed of the stream is 4km/hr.