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One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in:
- a)144 min
- b)180 min
- c)126 min
- d)114 min
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
One pipe can fill a tank four times as fast as another pipe. If togeth...
Suppose the slower pipe can fill the tank in x minutes.
Then the faster pipe can fill in x/4 minutes.
Part filled by the slower pipe in 1 min =1/x
Part filled by the faster pipe in 1 min =4/x
Part filled by the both the pipes in 1 min =1/x +4/x
Therefore, both the pipes can fill together in 36 minutes.
Part filled by both in 1 minute = 1/36.
1/x + 4/x = 1/36
5/x = 1/36
x = 5 * 36 = 180
Then the faster pipe can fill in x/4 minutes.
Part filled by the slower pipe in 1 min =1/x
Part filled by the faster pipe in 1 min =4/x
Part filled by the both the pipes in 1 min =1/x +4/x
Therefore, both the pipes can fill together in 36 minutes.
Part filled by both in 1 minute = 1/36.
1/x + 4/x = 1/36
5/x = 1/36
x = 5 * 36 = 180
Most Upvoted Answer
One pipe can fill a tank four times as fast as another pipe. If togeth...
Given information:
- One pipe fills the tank 4 times slower than the other pipe.
- Together, they can fill the tank in 36 minutes.
To find:
- The time taken by the slower pipe alone to fill the tank.
Solution:
Let's assume that the faster pipe can fill the tank in x minutes.
Then, the slower pipe can fill the tank in 4x minutes. (Given: one pipe fills 4 times slower than the other)
The amount of work done by the faster pipe in 1 minute = 1/x
The amount of work done by the slower pipe in 1 minute = 1/4x
When both pipes work together, they fill the tank in 36 minutes. So, the amount of work done by both pipes together in 1 minute = 1/36.
Using the above information, we can form an equation as follows:
1/x + 1/4x = 1/36
(Adding the amount of work done by both pipes in 1 minute)
Simplifying the equation, we get:
5/4x = 1/36
(Combining like terms)
x = 180
(Multiplying both sides by 4x and then dividing by 5)
Therefore, the faster pipe can fill the tank in 180 minutes.
Now, we need to find the time taken by the slower pipe alone to fill the tank.
As we know, the slower pipe can fill the tank in 4x minutes. So,
Time taken by slower pipe alone = 4x = 4 × 180 = 720 minutes
Therefore, the slower pipe alone will be able to fill the tank in 720 minutes, which is equivalent to 180 minutes or 3 hours.
Hence, the correct answer is option (B) 180 min.
- One pipe fills the tank 4 times slower than the other pipe.
- Together, they can fill the tank in 36 minutes.
To find:
- The time taken by the slower pipe alone to fill the tank.
Solution:
Let's assume that the faster pipe can fill the tank in x minutes.
Then, the slower pipe can fill the tank in 4x minutes. (Given: one pipe fills 4 times slower than the other)
The amount of work done by the faster pipe in 1 minute = 1/x
The amount of work done by the slower pipe in 1 minute = 1/4x
When both pipes work together, they fill the tank in 36 minutes. So, the amount of work done by both pipes together in 1 minute = 1/36.
Using the above information, we can form an equation as follows:
1/x + 1/4x = 1/36
(Adding the amount of work done by both pipes in 1 minute)
Simplifying the equation, we get:
5/4x = 1/36
(Combining like terms)
x = 180
(Multiplying both sides by 4x and then dividing by 5)
Therefore, the faster pipe can fill the tank in 180 minutes.
Now, we need to find the time taken by the slower pipe alone to fill the tank.
As we know, the slower pipe can fill the tank in 4x minutes. So,
Time taken by slower pipe alone = 4x = 4 × 180 = 720 minutes
Therefore, the slower pipe alone will be able to fill the tank in 720 minutes, which is equivalent to 180 minutes or 3 hours.
Hence, the correct answer is option (B) 180 min.
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