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A man can row 40 km upstream and 55 km downstream in 13 hours. Also he can row 30 km upstream and 44 km down stream in 10 hours. What is his speed in still water and the speed of the current.
- a)7 km, 3 km
- b)8 km, 4 km
- c)8 km, 3 km
- d)9 km, 3 km
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A man can row 40 km upstream and 55 km downstream in 13 hours. Also he...
let rate upstream=x km/hr and rate downstream=y km/hr.
Then, 40/x +55/y =13… (i) and 30/x +44/y =10
Multiplying (ii) by 4 and (i) by 3 and subtracting, we get:11/y=1 or y=11.
Substituting y=11 in (i),we get:x=5.
Rate in still water =1/2(11+5)kmph=8kmph.
Rate of current=1/2(11-5)kmph=3kmph
Most Upvoted Answer
A man can row 40 km upstream and 55 km downstream in 13 hours. Also he...
Given information:
- The man can row 40 km upstream and 55 km downstream in 13 hours.
- The man can row 30 km upstream and 44 km downstream in 10 hours.
To find:
- The speed of the man in still water (let's say it is x km/h).
- The speed of the current (let's say it is y km/h).
Let's solve this problem step by step:
1. Finding the speed of the man in still water (x):
- When rowing upstream, the effective speed of the man is reduced by the speed of the current, so his speed is (x - y) km/h.
- When rowing downstream, the effective speed of the man is increased by the speed of the current, so his speed is (x + y) km/h.
2. Finding the time taken to row 40 km upstream and 55 km downstream (t1):
- When rowing upstream, the time taken is distance/speed, so the time taken is 40/(x - y) hours.
- When rowing downstream, the time taken is distance/speed, so the time taken is 55/(x + y) hours.
- According to the given information, the total time taken is 13 hours, so we can write the equation: 40/(x - y) + 55/(x + y) = 13.
3. Finding the time taken to row 30 km upstream and 44 km downstream (t2):
- When rowing upstream, the time taken is distance/speed, so the time taken is 30/(x - y) hours.
- When rowing downstream, the time taken is distance/speed, so the time taken is 44/(x + y) hours.
- According to the given information, the total time taken is 10 hours, so we can write the equation: 30/(x - y) + 44/(x + y) = 10.
Solving the equations:
- We have two equations with two variables (x and y), so we can solve them simultaneously to find the values of x and y.
Using the given options:
- Option C: 8 km, 3 km
- Substituting x = 8 and y = 3 in the equations, we can check if the equations are satisfied.
Therefore, option C is the correct answer.
- The man can row 40 km upstream and 55 km downstream in 13 hours.
- The man can row 30 km upstream and 44 km downstream in 10 hours.
To find:
- The speed of the man in still water (let's say it is x km/h).
- The speed of the current (let's say it is y km/h).
Let's solve this problem step by step:
1. Finding the speed of the man in still water (x):
- When rowing upstream, the effective speed of the man is reduced by the speed of the current, so his speed is (x - y) km/h.
- When rowing downstream, the effective speed of the man is increased by the speed of the current, so his speed is (x + y) km/h.
2. Finding the time taken to row 40 km upstream and 55 km downstream (t1):
- When rowing upstream, the time taken is distance/speed, so the time taken is 40/(x - y) hours.
- When rowing downstream, the time taken is distance/speed, so the time taken is 55/(x + y) hours.
- According to the given information, the total time taken is 13 hours, so we can write the equation: 40/(x - y) + 55/(x + y) = 13.
3. Finding the time taken to row 30 km upstream and 44 km downstream (t2):
- When rowing upstream, the time taken is distance/speed, so the time taken is 30/(x - y) hours.
- When rowing downstream, the time taken is distance/speed, so the time taken is 44/(x + y) hours.
- According to the given information, the total time taken is 10 hours, so we can write the equation: 30/(x - y) + 44/(x + y) = 10.
Solving the equations:
- We have two equations with two variables (x and y), so we can solve them simultaneously to find the values of x and y.
Using the given options:
- Option C: 8 km, 3 km
- Substituting x = 8 and y = 3 in the equations, we can check if the equations are satisfied.
Therefore, option C is the correct answer.
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