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A man goes 80 km downstream and returns to the starting point in a total of 6 hours. If the ratio of the upstream speed to the downstream speed is 1 : 5, what is the speed of the stream?
- a)24 km/hr
- b)30 km/hr
- c)32 km/hr
- d)36 km/hr
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A man goes 80 km downstream and returns to the starting point in a tot...
Let the upstream speed = x km/hr
Downstream speed = 5x km/hr
96 = 6x
x = 16
Hence, Option C is correct.
Downstream speed = 5x km/hr
96 = 6x
x = 16
Hence, Option C is correct.
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Community Answer
A man goes 80 km downstream and returns to the starting point in a tot...
Understanding the Problem:
Given:
- Total time taken to go downstream and return upstream = 6 hours
- Ratio of upstream speed to downstream speed = 1 : 5
- Distance traveled downstream = Distance traveled upstream = 80 km
Let's solve the problem step by step:
1. Let the speed of the stream be S km/hr
2. Speed downstream = (S + D) km/hr
Speed upstream = (S - D) km/hr
(where D is the speed of the boat in still water)
3. Time taken to go downstream = 80 / (S + D) hours
Time taken to go upstream = 80 / (S - D) hours
4. Given total time taken is 6 hours:
80 / (S + D) + 80 / (S - D) = 6
5. Substitute the ratio of upstream speed to downstream speed (1:5):
(S - D) / (S + D) = 1/5
Solving, we get S = 6D
6. Substitute S = 6D in the total time equation:
80 / (6D + D) + 80 / (6D - D) = 6
Simplifying, we get D = 4 km/hr
7. Substitute D = 4 km/hr in S = 6D:
S = 6 * 4 = 24 km/hr
Therefore, the speed of the stream is 24 km/hr, which is option (c).
Given:
- Total time taken to go downstream and return upstream = 6 hours
- Ratio of upstream speed to downstream speed = 1 : 5
- Distance traveled downstream = Distance traveled upstream = 80 km
Let's solve the problem step by step:
1. Let the speed of the stream be S km/hr
2. Speed downstream = (S + D) km/hr
Speed upstream = (S - D) km/hr
(where D is the speed of the boat in still water)
3. Time taken to go downstream = 80 / (S + D) hours
Time taken to go upstream = 80 / (S - D) hours
4. Given total time taken is 6 hours:
80 / (S + D) + 80 / (S - D) = 6
5. Substitute the ratio of upstream speed to downstream speed (1:5):
(S - D) / (S + D) = 1/5
Solving, we get S = 6D
6. Substitute S = 6D in the total time equation:
80 / (6D + D) + 80 / (6D - D) = 6
Simplifying, we get D = 4 km/hr
7. Substitute D = 4 km/hr in S = 6D:
S = 6 * 4 = 24 km/hr
Therefore, the speed of the stream is 24 km/hr, which is option (c).
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A man goes 80 km downstream and returns to the starting point in a total of 6 hours. If the ratio of the upstream speed to the downstream speed is 1 : 5, what is the speed of the stream?a)24 km/hrb)30 km/hrc)32 km/hrd)36 km/hrCorrect answer is option 'C'. Can you explain this answer?
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