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To go a certain distance of 40 km upstream a rower takes 8 hours while it takes her only 5 hours to row the same distance downstream. What was the rower’s speed in still water?
- a)1.5 km/h
- b)4.5 km/h
- c)6.5 km/h
- d)4 km/h
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
To go a certain distance of 40 km upstream a rower takes 8 hours while...
Let x be the rower’s speed and y be the current speed of water.
Speed while going upstream = (x –y)
⇒ 40/ (x – y) = 8
⇒ x – y = 5 ---- (1)
Now speed while going downstream = (x + y)
⇒ 40/ (x + y) = 5
⇒ x + y = 8 ----(2)
From equation 1 and 2 we get
x = 6.5 km/hr
∴ Rower’s speed = 6.5 km/hr
Most Upvoted Answer
To go a certain distance of 40 km upstream a rower takes 8 hours while...
The rower's speed in still water is the average of her speed upstream and downstream.
Let's denote the rower's speed in still water as V, and the speed of the current as C.
When rowing upstream, the rower's effective speed (relative to the ground) is V - C.
When rowing downstream, the rower's effective speed is V + C.
We are given that it takes 8 hours to row 40 km upstream, so we can set up the equation:
(V - C) * 8 = 40
Similarly, we are given that it takes 5 hours to row 40 km downstream, so we can set up another equation:
(V + C) * 5 = 40
Solving these equations simultaneously will give us the values of V and C.
Expanding the first equation, we get:
8V - 8C = 40
Expanding the second equation, we get:
5V + 5C = 40
Now we have a system of equations:
8V - 8C = 40
5V + 5C = 40
Let's multiply the second equation by -8 to eliminate C:
-40V - 40C = -320
Adding this equation to the first equation, we get:
-40V - 40C + 8V - 8C = -320 + 40
-32V - 48C = -280
Dividing both sides by -8, we get:
4V + 6C = 35
Now we have another equation:
4V + 6C = 35
8V - 8C = 40
Let's multiply the first equation by 2 to eliminate V:
8V + 12C = 70
Adding this equation to the second equation, we get:
8V - 8C + 8V + 12C = 40 + 70
16V + 4C = 110
Dividing both sides by 4, we get:
4V + C = 27.5
Now we have another equation:
4V + C = 27.5
4V + 6C = 35
Subtracting the first equation from the second equation, we get:
4V + 6C - (4V + C) = 35 - 27.5
5C = 7.5
Dividing both sides by 5, we get:
C = 1.5
Substituting this value of C into the first equation, we get:
4V + 1.5 = 27.5
Subtracting 1.5 from both sides, we get:
4V = 26
Dividing both sides by 4, we get:
V = 6.5
Therefore, the rower's speed in still water is 6.5 km/h and the speed of the current is 1.5 km/h.
Let's denote the rower's speed in still water as V, and the speed of the current as C.
When rowing upstream, the rower's effective speed (relative to the ground) is V - C.
When rowing downstream, the rower's effective speed is V + C.
We are given that it takes 8 hours to row 40 km upstream, so we can set up the equation:
(V - C) * 8 = 40
Similarly, we are given that it takes 5 hours to row 40 km downstream, so we can set up another equation:
(V + C) * 5 = 40
Solving these equations simultaneously will give us the values of V and C.
Expanding the first equation, we get:
8V - 8C = 40
Expanding the second equation, we get:
5V + 5C = 40
Now we have a system of equations:
8V - 8C = 40
5V + 5C = 40
Let's multiply the second equation by -8 to eliminate C:
-40V - 40C = -320
Adding this equation to the first equation, we get:
-40V - 40C + 8V - 8C = -320 + 40
-32V - 48C = -280
Dividing both sides by -8, we get:
4V + 6C = 35
Now we have another equation:
4V + 6C = 35
8V - 8C = 40
Let's multiply the first equation by 2 to eliminate V:
8V + 12C = 70
Adding this equation to the second equation, we get:
8V - 8C + 8V + 12C = 40 + 70
16V + 4C = 110
Dividing both sides by 4, we get:
4V + C = 27.5
Now we have another equation:
4V + C = 27.5
4V + 6C = 35
Subtracting the first equation from the second equation, we get:
4V + 6C - (4V + C) = 35 - 27.5
5C = 7.5
Dividing both sides by 5, we get:
C = 1.5
Substituting this value of C into the first equation, we get:
4V + 1.5 = 27.5
Subtracting 1.5 from both sides, we get:
4V = 26
Dividing both sides by 4, we get:
V = 6.5
Therefore, the rower's speed in still water is 6.5 km/h and the speed of the current is 1.5 km/h.
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To go a certain distance of 40 km upstream a rower takes 8 hours while it takes her only 5 hours to row the same distance downstream. What was the rower’s speed in still water?a)1.5 km/hb)4.5 km/hc)6.5 km/hd)4 km/hCorrect answer is option 'C'. Can you explain this answer?
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