Pipe X can fill a tank in 60 hours while pipe Y can fill the tank in 72 hours. Both pipes are opened together for 20 hours. How much of the tank is left empty?

Question

Accepted Answer

Step 1: Calculate the rate of filling for each pipe.
- Pipe X fills the tank in 60 hours, so its rate is 1/60 tank per hour.
- Pipe Y fills the tank in 72 hours, so its rate is 1/72 tank per hour.

Step 2: Calculate the combined rate when both pipes are opened together.
Combined rate = 1/60 + 1/72
To add, find the LCM of 60 and 72.
- Prime factors:
  60 = 2^2 * 3 * 5
  72 = 2^3 * 3^2
LCM = 2^3 * 3^2 * 5 = 8 * 9 * 5 = 360

Convert rates to have denominator 360:
- 1/60 = 6/360
- 1/72 = 5/360
Combined rate = 6/360 + 5/360 = 11/360 tank per hour.

Step 3: Calculate how much of the tank is filled in 20 hours.
Amount filled = rate * time = (11/360) * 20 = 220/360 = 11/18.

Step 4: Calculate how much of the tank is left empty.
Empty part = 1 - 11/18 = 7/18.

Therefore, the fraction of the tank left empty after 20 hours is 7/18.

Answer

Answer

Answer