a tank of 100litres has two taps one tap pours in 60L in 5mins and takes out 14L in 2mins. find the time taken to fill that tank when both taps are open
Divide the volume (L) by the net fill rate (L/min):
100/(60/5 - 14/2) = 20 min
60 L in 5 min ----> 12 L in 1 minute = input
14 L in 2 min ----> 7 L in 1 minute = output
net input = 5 L/min
time to fill 100L
= 100/5 L/min
= 20 minutes
To find the time taken to fill the tank when both taps are open, we need to determine the net inflow of water per minute.
First, let's find the net inflow of water from each tap:
- The first tap pours in 60 liters in 5 minutes, so the inflow rate of the first tap is 60 liters / 5 minutes = 12 liters per minute.
- The second tap takes out 14 liters in 2 minutes, so the outflow rate of the second tap is 14 liters / 2 minutes = 7 liters per minute.
To find the net inflow, we subtract the outflow rate from the inflow rate:
Net inflow rate = Inflow rate - Outflow rate
Net inflow rate = 12 liters per minute - 7 liters per minute
Net inflow rate = 5 liters per minute
Since both taps are open, the net inflow rate will be the sum of the individual inflow rates:
Net inflow rate (when both taps are open) = 12 liters per minute + 7 liters per minute
Net inflow rate (when both taps are open) = 19 liters per minute
Now, to find the time taken to fill the tank, we can divide the total volume of the tank (100 liters) by the net inflow rate:
Time taken to fill the tank = Tank volume / Net inflow rate
Time taken to fill the tank = 100 liters / 19 liters per minute
Calculating this, we find:
Time taken to fill the tank ≈ 5.26 minutes
Therefore, it will take approximately 5.26 minutes to fill the tank when both taps are open.