If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how lo

If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?

If pipe A can fill a tank in 10 hours and pipe B can fill it in 15 hours, how long will it take to fill the tank if both pipes are opened together?

Correct Answer: 6 hours

Step 1: Determine the rate at which pipe A fills the tank. Since it can fill the tank in 10 hours, its rate is 1 tank per 10 hours, or 1/10 of the tank per hour.
Step 2: Determine the rate at which pipe B fills the tank. Since it can fill the tank in 15 hours, its rate is 1 tank per 15 hours, or 1/15 of the tank per hour.
Step 3: Add the rates of both pipes together to find the combined rate. This is done by calculating 1/10 + 1/15.
Step 4: To add 1/10 and 1/15, find a common denominator. The least common multiple of 10 and 15 is 30.
Step 5: Convert 1/10 to a fraction with a denominator of 30. This is 3/30.
Step 6: Convert 1/15 to a fraction with a denominator of 30. This is 2/30.
Step 7: Now add the two fractions: 3/30 + 2/30 = 5/30.
Step 8: Simplify 5/30 to 1/6. This means together, both pipes can fill 1/6 of the tank in one hour.
Step 9: To find out how long it takes to fill the entire tank, take the reciprocal of 1/6. This gives you 6 hours.

Rate of Work – Understanding how to calculate the combined work rate of multiple entities working together.
Fraction Addition – Applying the concept of adding fractions to determine the total rate of filling the tank.