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At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours lessthan it takes him to travel the same distance upstream. But if he could double his usual rowing ratefor his 24‐mile round trip, the downstream 12 miles would then take only one hour less than theupstream 12 miles. What is the speed of the current in miles per hour?
- a)2*1/3 mph
- b)1*1/3 mph
- c)1*2/3 mph
- d)2*2/3 mph
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
At his usual rowing rate, Rahul can travel 12 miles downstream in a ce...
Option D
Explanation :Let the speed of Rahul in still water be x mphand the speed of the current be y mphThen, Speed upstream = (x ‐ y) mphSpeed downstream = (x + y) mphDistance = 12 milesTime taken to travel upstream ‐ Time taken to travel downstream = 6 hours⇒12/(x−y)−12/(x+y)=6⇒12(x+y)−12(x−y)=6(x*x−y*y)⇒24y=6(x*x−y*y)⇒4y= x*x−y*y⇒x * x =(y* y +4y)⋯(Equation 1)Now he doubles his speed. i.e., his new speed = 2xNow, Speed upstream = (2x ‐ y) mphSpeed downstream = (2x + y) mphIn this case, Time taken to travel upstream ‐ Time taken to travel downstream = 1 hour⇒12/(2x−y)−12/(2x+y)=1⇒12(2x+y)−12(2x−y)=4*x* x –y* y⇒24y=4*x* x –y* y⇒4*x* x = y* y +24y⋯(Equation 2)(Equation 1 × 4)⇒4x* x =4(y* y +4y)⋯(Equation 3)(From Equation 2 and 3, we have)y* y +24y=4(y* y +4y) ⇒y* y +24y=4y* y +16y ⇒3y* y =8y ⇒3y=8y=8/3 mph i.e., speed of the current = 8/3 mph=2*2/3 mph
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At his usual rowing rate, Rahul can travel 12 miles downstream in a ce...
Given information:
- Rahul can travel 12 miles downstream in 6 hours less than it takes him to travel the same distance upstream.
- If Rahul could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles.
Let's assume Rahul's usual rowing rate is 'r' mph (miles per hour) and the speed of the current is 'c' mph.
Distance and time calculations:
- When Rahul rows downstream, his effective speed is r + c mph.
- When Rahul rows upstream, his effective speed is r - c mph.
First scenario: Traveling downstream
- Distance: 12 miles
- Speed: r + c mph
- Time: T1 hours
According to the given information, Rahul can travel 12 miles downstream in 6 hours less than it takes him to travel the same distance upstream. Therefore, the time taken downstream is T1 hours and the time taken upstream is T1 + 6 hours.
Second scenario: Traveling upstream
- Distance: 12 miles
- Speed: r - c mph
- Time: T1 + 6 hours
Third scenario: Round trip with doubled rowing rate
- Distance: 24 miles
- Speed downstream: 2r + c mph
- Speed upstream: 2r - c mph
- Time downstream: T1 - 1 hour (one hour less than the upstream time)
- Time upstream: T1 + 6 hours (same as the previous scenario)
Calculating the time taken:
- For the first scenario (downstream), using the formula: Time = Distance / Speed
- T1 = 12 / (r + c)
- For the second scenario (upstream), using the formula: Time = Distance / Speed
- T1 + 6 = 12 / (r - c)
- For the third scenario (round trip downstream), using the formula: Time = Distance / Speed
- T1 - 1 = 12 / (2r + c)
- For the third scenario (round trip upstream), using the formula: Time = Distance / Speed
- T1 + 6 = 12 / (2r - c)
Solving the equations:
From the equations, we can form the following equations:
- T1 = 12 / (r + c)
- T1 + 6 = 12 / (r - c)
- T1 - 1 = 12 / (2r + c)
- T1 + 6 = 12 / (2r - c)
By solving these equations, we can find the values of r and c.
Calculating the speed of the current:
After solving the equations, we find that the speed of the current (c) is equal to 2/3 mph.
Therefore, the correct answer is option 'D': 2 * 2/3 mph.
- Rahul can travel 12 miles downstream in 6 hours less than it takes him to travel the same distance upstream.
- If Rahul could double his usual rowing rate for his 24-mile round trip, the downstream 12 miles would then take only one hour less than the upstream 12 miles.
Let's assume Rahul's usual rowing rate is 'r' mph (miles per hour) and the speed of the current is 'c' mph.
Distance and time calculations:
- When Rahul rows downstream, his effective speed is r + c mph.
- When Rahul rows upstream, his effective speed is r - c mph.
First scenario: Traveling downstream
- Distance: 12 miles
- Speed: r + c mph
- Time: T1 hours
According to the given information, Rahul can travel 12 miles downstream in 6 hours less than it takes him to travel the same distance upstream. Therefore, the time taken downstream is T1 hours and the time taken upstream is T1 + 6 hours.
Second scenario: Traveling upstream
- Distance: 12 miles
- Speed: r - c mph
- Time: T1 + 6 hours
Third scenario: Round trip with doubled rowing rate
- Distance: 24 miles
- Speed downstream: 2r + c mph
- Speed upstream: 2r - c mph
- Time downstream: T1 - 1 hour (one hour less than the upstream time)
- Time upstream: T1 + 6 hours (same as the previous scenario)
Calculating the time taken:
- For the first scenario (downstream), using the formula: Time = Distance / Speed
- T1 = 12 / (r + c)
- For the second scenario (upstream), using the formula: Time = Distance / Speed
- T1 + 6 = 12 / (r - c)
- For the third scenario (round trip downstream), using the formula: Time = Distance / Speed
- T1 - 1 = 12 / (2r + c)
- For the third scenario (round trip upstream), using the formula: Time = Distance / Speed
- T1 + 6 = 12 / (2r - c)
Solving the equations:
From the equations, we can form the following equations:
- T1 = 12 / (r + c)
- T1 + 6 = 12 / (r - c)
- T1 - 1 = 12 / (2r + c)
- T1 + 6 = 12 / (2r - c)
By solving these equations, we can find the values of r and c.
Calculating the speed of the current:
After solving the equations, we find that the speed of the current (c) is equal to 2/3 mph.
Therefore, the correct answer is option 'D': 2 * 2/3 mph.
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At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hours lessthan it takes him to travel the same distance upstream. But if he could double his usual rowing ratefor his 24‐mile round trip, the downstream 12 miles would then take only one hour less than theupstream 12 miles. What is the speed of the current in miles per hour?a)2*1/3 mphb)1*1/3 mphc)1*2/3 mphd)2*2/3 mphCorrect answer is option 'D'. Can you explain this answer?
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