If a cistern is filled by two pipes A and B in 12 hours and 15 hours respectivel
Practice Questions
Q1
If a cistern is filled by two pipes A and B in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?
6 hours
7.2 hours
8 hours
9 hours
Questions & Step-by-Step Solutions
If a cistern is filled by two pipes A and B in 12 hours and 15 hours respectively, how long will it take to fill the cistern if both pipes are opened together?
Step 1: Determine the rate at which pipe A fills the cistern. Since it takes 12 hours to fill the cistern, the rate is 1/12 of the cistern per hour.
Step 2: Determine the rate at which pipe B fills the cistern. Since it takes 15 hours to fill the cistern, the rate is 1/15 of the cistern per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/12 + 1/15.
Step 4: To add 1/12 and 1/15, find a common denominator. The least common multiple of 12 and 15 is 60.
Step 5: Convert 1/12 to a fraction with a denominator of 60: 1/12 = 5/60.
Step 6: Convert 1/15 to a fraction with a denominator of 60: 1/15 = 4/60.
Step 7: Now add the two fractions: 5/60 + 4/60 = 9/60.
Step 8: Simplify 9/60 to 3/20. This means together, both pipes fill 3/20 of the cistern in one hour.
Step 9: To find out how long it takes to fill the entire cistern, take the reciprocal of the combined rate: 1 / (3/20) = 20/3 hours.
Step 10: Convert 20/3 hours into a more understandable format. 20/3 hours is approximately 6.67 hours.
Work Rate – Understanding how to calculate the combined work rate of multiple entities working together.
Fraction Addition – Adding fractions with different denominators to find a common rate.
Time Calculation – Calculating the total time taken based on the combined work rate.
