Arjun opens hot water pipe of diameter 6 cm and cold water pipe of diameter 3 cm in order to fill a bathtub of volume 60cm*20 cm* 10 cm at 9:00 a.m. when he turns at 9.16 a.m. he notices that only one third of the tub is full as he had forgotten to close the drain pipe he closes it immediately given that the hot water pipe can fill the hub by itself in 48 minutes how long it the drain pipe take to empty a full tub
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Answer:
192 Mins
Step-by-step explanation:
hot water pipe can fill the Tub by itself in 48 minutes
=> hot water pipe can fill the Tub in 1 Minute = 1/48
hot water pipe of diameter 6 cm => area = π (6/2)² = 9π cm²
Cold water pipe of diameter 3 cm => area = π (3/2)² = 9π/4 cm²
=>cold water pipe can fill the Tub in 1 Minute = (1/48) * (9π/4)/9π = 1/192
Hot pipe + cold pipe together can fill in1 min = 1/48 + 1/192
= (5/192)
Hot pipe + cold pipe together can fill in 16 min ( 9:00 - 9:16)
= 16 * 5/192
=> 5/12
Tub filled = 1/3
Tub emptied by drain pipe in 16 mins = 5/12 - 1/3 = (5 - 4)/12 = 1/12
Tub emptied by drain pipe in 1 min = 1/192
drain pipe take time to empty a full tub = 192 Mins
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