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

Solution:

Let us consider the speed of the motorboat in still water to be u km/hr.

Let us consider the speed of the stream to be ν km/h.

downstream speed of motorboat = (u + ν) km/h

upstream speed of motorboat = (u - ν) km/h.

Time taken to travel 30 km upstream,

t₁ = 30/u-v hours

Time taken to travel 28km downstream,

t₂ = 28/u+v hours.

As per the first condition,

t₁ + t₂ = 7 hours

30/u-v + 28/u+v = 7------------------------------------------(1)

Time taken to travel 21 km upstream,

t₃ = 21/u-v hours.

Time taken to travel 21 km downstream,

t₄ = 21/u+v hours.

As per the second condition,

t₄ + t₃ = 5 hours

21/u+v + 21/u+v = 5------------------------------------------(2)

Let us consider,

x = 1/u+v

y = 1/u-v

Rearranging (1) and (2), we get,

30x + 28y = 7---------------------------------------------------(3)

21x + 21y = 5---------------------------------------------------(4)

x + y = 5/21.

Solve the linear equations (3) and (4)

Multiplying equation (4) by 28 and then subtracting from (3), we get,

(30x - 28y) - (28x + 28y) = 7 - 140/21

2x = 7 - 20/3

2x = 1/3

x = 1/6.

Substituting the value of x in(4), we get,

1/6 + y = 5/21

y = 5/21 = 1/6 = 10 -7/42 = 3/42

y = 1/14.

x = 1/u+v = 1/6

u + v = 6---------------------------(5)

y = 1/u-v = 1/14

u-v = 14----------------------------(6)

Adding (5) and (6), we get,

2u = 20

u = 10.

Substituting the value of u in (5),we get,

10 + ν = 6

ν = -4.

u = 10.

ν = -4.

Therefore, the speed of the motorboat in still water is 10 km/h and the speed of the stream 4 km/h.

✦ Try This: A motorboat can travel 20 km upstream and 18 km downstream in 5 hours. It can travel 11 km upstream and return in 3 hours. Find the speed of the boat in still water and the speed of the stream

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 3

NCERT Exemplar Class 10 Maths Exercise 3.4 Problem 8

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

Summary:

A motorboat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. The speed of the motorboat in still water is 10 km/h and the speed of the stream 4 km/h.

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