Swati can row her boat at a speed of 5 km/hr in still water. If it takes her 1 hour more to row the boat 5.25 km upstream than to return downstream, find the speed of the stream.a)5 km/hrb)2 km/hrc)3 km/hrd)4 km/hrCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let the speed of the stream be x km/h
Speed of the boat in upstream = (5 - x)km/h
Speed of the boat in downstream = (5 + x)km/h
Time, say t₁ (in hours), for going 5.25 km upstream = 5.25/5 - x
Time, say t₂ (in hours), for returning 5.25 km downstream = 5.25/5 + x
Obviously t₁ > t₂
Therefore, according to the given condition of the problem,
t₁ = t₂ + 1

This gives x = 2, since we reject x = -25/2
Thus, the speed of the stream is 2 km/h.

Answer

To solve this problem, we need to use the concept of relative speed and the formula for time, speed, and distance. Let's break down the problem step by step.

Given:
- Swati can row her boat at a speed of 5 km/hr in still water.
- It takes her 1 hour more to row the boat 5.25 km upstream than to return downstream.

Let's assume the speed of the stream is 's' km/hr.

Finding the downstream speed:
When Swati rows downstream, her effective speed will be the sum of her rowing speed and the speed of the stream. So, her downstream speed will be (5 + s) km/hr.

Finding the upstream speed:
When Swati rows upstream, her effective speed will be the difference between her rowing speed and the speed of the stream. So, her upstream speed will be (5 - s) km/hr.

Using the formula for time, speed, and distance:
We know that time = distance/speed.

Let's calculate the time taken to row downstream:
Distance = 5.25 km
Speed = (5 + s) km/hr
Time taken downstream = Distance/Speed = 5.25/(5 + s) hr

Now, let's calculate the time taken to row upstream:
Distance = 5.25 km
Speed = (5 - s) km/hr
Time taken upstream = Distance/Speed = 5.25/(5 - s) hr

According to the given information, it takes 1 hour more to row upstream than to row downstream. So, we can write the equation:

Time taken upstream = Time taken downstream + 1
5.25/(5 - s) = 5.25/(5 + s) + 1

Simplifying the equation:
5.25(5 + s) = 5.25(5 - s) + (5 - s)(5 + s)
26.25 + 5.25s = 26.25 - 5.25s + 25 - s^2
10.5s = 25 - s^2
s^2 + 10.5s - 25 = 0

Using the quadratic formula:
s = (-b ± √(b^2 - 4ac))/2a
s = (-10.5 ± √(10.5^2 - 4(1)(-25)))/(2(1))
s = (-10.5 ± √(110.25 + 100))/2
s = (-10.5 ± √210.25)/2
s = (-10.5 ± 14.5)/2

Simplifying further:
s = (-10.5 + 14.5)/2 or s = (-10.5 - 14.5)/2
s = 4/2 or s = -25/2 (rejecting the negative value)

Therefore, the speed of the stream is 2 km/hr (option B).

Top Courses for Class 10View all

Science Class 10

Social Studies (SST) Class 10

Mathematics (Maths) Class 10

Past Year Papers for Class 10

English Class 10

Top Courses for Class 10

Top Courses for Class 10

Related Content

About Class 10

Class 10 Study Material

Class 10 All Subjects

NCERT Textbook Solutions

Other Classes

Important Links

Company