A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the same river. If the speed of the river is 4 km/h, find the speed of the boat in still water.?

Question

Answer

Problem:
A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the same river. If the speed of the river is 4 km/h, find the speed of the boat in still water.

Solution:
Let the speed of the boat be 'x' km/h and the speed of the river be 'y' km/h.

Step 1: Write the formula for time taken to travel a certain distance.
Time = Distance/Speed

Step 2: Find the time taken to travel 30 km upstream.
Time taken to travel upstream = 30/(x-y)

Step 3: Find the time taken to travel 60 km downstream.
Time taken to travel downstream = 60/(x+y)

Step 4: Since both the times are equal, we can equate the two expressions.
30/(x-y) = 60/(x+y)

Step 5: Simplify the above expression to get an equation in 'x' and 'y'.
x^2 - y^2 = 45

Step 6: Substitute the value of 'y' in terms of the given speed of the river.
y = 4 km/h (Given)

Step 7: Simplify the equation to get an expression in terms of 'x'.
x^2 - 16 = 45

Step 8: Solve for 'x'.
x^2 = 61
x = √61 km/h

Step 9: Round off the answer to one decimal place.
x ≈ 7.8 km/h

Answer: The speed of the boat in still water is approximately 7.8 km/h.

Answer

Let the speed in still water is 'xkm/h'

So downstream speed =[x+4]km/h

and up stream speed =[x-4]km/h

So;downstream time taken to cover=60km/h

=distance/downstream speed =60/x+4 hours

for up stream=30/x-4 hours

time is same so

60/x+4=30/x-4

2/x+4=1/x-4

2x-8=x+4

2x-x=8+4

x=12km/h

Similar Class 8 Doubts

A boat travels 30 km upstream in the same amount of time it takes to travel 60 km downstream in the river. If the speed of the river is 4 km/h , find the speed of the boat in still water?

A steamer goes downstream from one port to another in 6 hours. It covers the same distance upstream in 7 hours. If the speed of the stream be 2km/hr , find the speed of the steamer in still water.?

Arrest boat covers a distance of 60 km downstream in one and half hour it covers distance upstream in 2 hours the speed of the boat in still water is 35 kilometre per hour find the speed of the stream?

Race boat covers a distance in 66 km downstream in 110 minutes it covers the distance upstream in in 120 minutes the speed of boat in still water is 34.5 km per hour find the speed of the stream?

A motor boat covers a certain distance downstream in a river in 5 hours cute cover the same distance upstream in 5 hours and a half the speed of water is 1.5 per kilometre find the speed of the boat in still water?

Top Courses for Class 8View all

Science Class 8

Mathematics (Maths) Class 8

Social Studies (SST) Class 8

English Class 8

Cursive Writing Course-Improve Your Handwriting

Top Courses for Class 8

Top Courses for Class 8

Suggested Free Tests

Related Content

Class 8 Study Material

Class 8 Subjects

Competitive Examinations for Class 8

NCERT Solutions

Reference Books for Class 8

Other Popular Exams

Company