A cylindrical water reservoir is served with 3 pumps P,Q,R. Pump P can fill the empty reservoir in 5 hours while pump Q can fill the same reservoir in 10 hours. When full pump R can drain the reservoir in3 hours. a) One day the reservoir was empty and pumps P and Q opened at 8.45am.At 11.15am pump P developed an electric fault .Pump Q continued operating alone till the reservoir was full.Find the time of the day that the reservoir was completely filled .b) On another day the reservoir was halfway filled with water .Pumps P and R were then opened at the same time. How long did it take to completely drain the reservoir. c) The reservoir's dimensions are base diameter 14 meters and height 12.5 meters . The water in (b)above is filled in a water tanker of capacity 12000 litres. How many trips does the tanker make to drain the reservoir.
a) From 8:45 am to 11:15 am is a total of 2.5 hours.
During this time, pump P can fill (1/5) * 2.5 = 0.5 of the reservoir.
Pump Q can fill (1/10) * 2.5 = 0.25 of the reservoir.
So in total, pumps P and Q can fill (0.5 + 0.25) = 0.75 of the reservoir in 2.5 hours.
Since pump Q continued operating alone after 11:15 am, we can consider pump Q as the only pump filling the reservoir.
To find the remaining portion of the reservoir to be filled, we subtract 0.75 from 1: 1 - 0.75 = 0.25.
Since pump Q can fill (1/10) of the reservoir in 1 hour, it will take (1 / (1/10)) * 0.25 = 2.5 hours.
Adding the time from 8:45 am to 11:15 am, the reservoir will be completely filled at 1:45 pm.
b) Since pump P can fill the reservoir in 5 hours and pump R can drain the reservoir in 3 hours, the combined rate of filling and draining is (1/5) - (1/3) = (3 - 5) / 15 = -2/15.
This means that the reservoir can be drained at a rate of (2/15) of its capacity per hour.
Since the reservoir is halfway filled, pump P and pump R need to drain (1/2) of the reservoir's capacity.
Using the rate of draining as calculated earlier, it will take (1/2) / (2/15) = (1/2) * (15/2) = 7.5 hours to completely drain the reservoir.
c) The volume of the reservoir can be calculated using the formula for the volume of a cylinder: V = π * r^2 * h, where r is the radius (half the base diameter) and h is the height.
Given the base diameter of 14 meters, the radius is 14 / 2 = 7 meters, and the height is 12.5 meters.
Using the formula, the volume of the reservoir is V = π * 7^2 * 12.5 = 1715.56 cubic meters.
Since 1 cubic meter is equal to 1000 liters, the capacity of the reservoir is 1715.56 * 1000 = 1715560 liters.
Dividing the capacity of the reservoir by the capacity of the water tanker (12000 liters), we get 1715560 / 12000 = 142.9633.
Therefore, the tanker will make 143 trips to drain the reservoir.