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Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town?
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Streamer going downstream in a river covers the distance between two t...
To find the distance between the two towns, we need to analyze the situation using the speeds of the streamer in both downstream and upstream conditions.
Understanding the Scenario
- The streamer travels downstream and upstream in a river.
- Time taken downstream = 15 hours.
- Time taken upstream = 20 hours.
- Speed of the water = 3 km/h.
Defining the Speeds
- Let the speed of the streamer in still water be \( S \) km/h.
- Downstream speed = \( S + 3 \) km/h (streamer speed plus water speed).
- Upstream speed = \( S - 3 \) km/h (streamer speed minus water speed).
Setting Up Equations
- Distance (D) between the two towns can be expressed as:
- Downstream: \( D = (S + 3) \times 15 \)
- Upstream: \( D = (S - 3) \times 20 \)
Equating the Distances
- Since both expressions equal the same distance \( D \):
\[
(S + 3) \times 15 = (S - 3) \times 20
\]
- Expanding both sides:
\[
15S + 45 = 20S - 60
\]
- Rearranging gives:
\[
20S - 15S = 60 + 45
\]
\[
5S = 105
\]
\[
S = 21 \text{ km/h}
\]
Calculating the Distance
- Substituting \( S \) back into the distance equation:
\[
D = (21 + 3) \times 15 = 24 \times 15 = 360 \text{ km}
\]
Conclusion
- The distance between the two towns is **360 km**.
Understanding the Scenario
- The streamer travels downstream and upstream in a river.
- Time taken downstream = 15 hours.
- Time taken upstream = 20 hours.
- Speed of the water = 3 km/h.
Defining the Speeds
- Let the speed of the streamer in still water be \( S \) km/h.
- Downstream speed = \( S + 3 \) km/h (streamer speed plus water speed).
- Upstream speed = \( S - 3 \) km/h (streamer speed minus water speed).
Setting Up Equations
- Distance (D) between the two towns can be expressed as:
- Downstream: \( D = (S + 3) \times 15 \)
- Upstream: \( D = (S - 3) \times 20 \)
Equating the Distances
- Since both expressions equal the same distance \( D \):
\[
(S + 3) \times 15 = (S - 3) \times 20
\]
- Expanding both sides:
\[
15S + 45 = 20S - 60
\]
- Rearranging gives:
\[
20S - 15S = 60 + 45
\]
\[
5S = 105
\]
\[
S = 21 \text{ km/h}
\]
Calculating the Distance
- Substituting \( S \) back into the distance equation:
\[
D = (21 + 3) \times 15 = 24 \times 15 = 360 \text{ km}
\]
Conclusion
- The distance between the two towns is **360 km**.
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Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town?
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Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town?.
Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Streamer going downstream in a river covers the distance between two towns and 15 hours coming back up stream it covers did distance in 20 hours the speed of the water is 3 km per hour find the distance between two town?.
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