Question

The cold water tap can fill a container two hours faster than the hot water tap. The two taps together can fill a container in 80 minutes. How long does it take each tap to fill the container on its own?

Answer 1

• 4 hours and 2 hours

Explanation:

Let the time for cold tap be c and hot tap be h.

Convert

• 2hrs = 120 min

Set equations

The cold water tap can fill a container two hours faster than the hot water tap:

• c - h = 120

The two taps together can fill a container in 80 minutes:

• 1/c + 1/h = 1/80

Solve the system by substitution

• c = h + 120

• 1/c + 1/h = 1/80
• 1/(h + 120) + 1/h = 1/80
• (h + h + 120)/(h(h+120)) = 1/80
• 80(2h + 120) = h(h + 120)
• 160h + 9600 = h² + 120h
• h² - 40h - 9600 = 0
• h² - 40h + 400 = 10000
• (h - 20)² = 100²
• h - 20 = 100 (taking positive root only, since time is positive value)
• h = 120 min = 2 hrs

Find c

• c = 120 + 120 = 240 min = 4 hrs