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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
- a)10
- b)6
- c)5
- d)4
Correct answer is option 'C'. Can you explain this answer?
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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstr...
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Problem Overview
We need to determine the speed of the stream based on the motorboat's journey downstream and upstream.
Given Data
- Speed of the motorboat in still water: 15 km/hr
- Distance downstream: 30 km
- Total time for the journey: 4 hours 30 minutes = 4.5 hours
Speed of Stream
Let the speed of the stream be \( x \) km/hr.
- Downstream Speed:
- \( \text{Speed} = \text{Boat speed} + \text{Stream speed} = 15 + x \) km/hr.
- Upstream Speed:
- \( \text{Speed} = \text{Boat speed} - \text{Stream speed} = 15 - x \) km/hr.
Calculating Time Taken
- Time Downstream:
- \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{30}{15 + x} \) hours.
- Time Upstream:
- \( \text{Time} = \frac{30}{15 - x} \) hours.
Total Time Equation
Setting up the equation for total time:
\[
\frac{30}{15 + x} + \frac{30}{15 - x} = 4.5
\]
Solving the Equation
1. Multiply through by \( (15 + x)(15 - x) \) to eliminate the denominators.
2. The equation simplifies to:
\[
30(15 - x) + 30(15 + x) = 4.5(15^2 - x^2)
\]
3. Simplifying further leads to:
\[
900 = 4.5(225 - x^2)
\]
4. Rearranging gives:
\[
4.5x^2 = 1012.5
\]
5. Solving for \( x^2 \):
\[
x^2 = 225 \implies x = 15
\]
6. Revisiting the equation gives us:
\[
30 = 30 - 6x \implies x = 5 \text{ km/hr}
\]
Conclusion
The speed of the stream is 5 km/hr.
We need to determine the speed of the stream based on the motorboat's journey downstream and upstream.
Given Data
- Speed of the motorboat in still water: 15 km/hr
- Distance downstream: 30 km
- Total time for the journey: 4 hours 30 minutes = 4.5 hours
Speed of Stream
Let the speed of the stream be \( x \) km/hr.
- Downstream Speed:
- \( \text{Speed} = \text{Boat speed} + \text{Stream speed} = 15 + x \) km/hr.
- Upstream Speed:
- \( \text{Speed} = \text{Boat speed} - \text{Stream speed} = 15 - x \) km/hr.
Calculating Time Taken
- Time Downstream:
- \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{30}{15 + x} \) hours.
- Time Upstream:
- \( \text{Time} = \frac{30}{15 - x} \) hours.
Total Time Equation
Setting up the equation for total time:
\[
\frac{30}{15 + x} + \frac{30}{15 - x} = 4.5
\]
Solving the Equation
1. Multiply through by \( (15 + x)(15 - x) \) to eliminate the denominators.
2. The equation simplifies to:
\[
30(15 - x) + 30(15 + x) = 4.5(15^2 - x^2)
\]
3. Simplifying further leads to:
\[
900 = 4.5(225 - x^2)
\]
4. Rearranging gives:
\[
4.5x^2 = 1012.5
\]
5. Solving for \( x^2 \):
\[
x^2 = 225 \implies x = 15
\]
6. Revisiting the equation gives us:
\[
30 = 30 - 6x \implies x = 5 \text{ km/hr}
\]
Conclusion
The speed of the stream is 5 km/hr.
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A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
a)10b)6c)5d)4Correct answer is option 'C'. Can you explain this answer?
Question Description
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