A tank when full can contain 1500 litres of water. Pump A can fill water into the tank at a rate of x litres per minute. If pump A takes 30 secons longer than pump B to fill in the tank completely, formulate an equation in x to represent this information and show that it reduces to x squared plus 50 x minus 150, 000
Answers
Given : A tank when full can contain 1500 litres of water. Pump A can fill water into the tank at a rate of x litres per minute.Pump b can fill water into the tank at a rate of (x+50) liters per minute.
pump A takes 30 secons longer than pump B to fill in the tank completely,
To Find : formulate an equation in x to represent this information
Solution:
A tank when full can contain 1500 litres of water.
A can fill water into the tank at a rate of x litres per minute
B can fill water into the tank at a rate of x+50 litres per minute
pump A takes 30 seconds longer than pump B to fill in the tank completely,
= 1/2 minutes
Let say A fills tank in t minutes => t = 1500/x
B fills tank in t - 1/2 minute
Time taken by B to fill tank = 1500/(x + 50)
=> 1500/(x + 50) = 1500/x - 1/2
=> 3000 x = 3000 (x + 50) - x(x + 50)
=> 0 = 150000 - x² - 50x
=> x² + 50x - 150000 = 0
QED
Hence proved
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