Answer :
Answer:
- 4 hours and 2 hours
Step-by-step 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