Two taps together can fill a tank completely in 40/13 minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?
Answers
Answer:
time taken by larger tap = 5 minutes
time taken by smaller tap = 8 minutes
Step-by-step explanation:
Let the larger tap takes x minutes to fill the tank
=> Tank filled by larger tap in 1 minute = 1/x
Time taken by the smaller tap to fill the tank = x + 3
=> Tank filled by smaller tap in 1 minute = 1/(x+3)
Given the total time taken to fill the tank together = 40/13 minutes
=> amount of tank filled in 1 minute = 13/40
=> 1/x + 1/(x+3) = 13/40
=> (2x+3)/(x²+3x) = 13/40
=> 13x² + 39x = 80x + 120
=> 13x² - 41x - 120 = 0
=> x = [41 ± √(41²+4.13.120)]/26
= [41 ± √(1681+6240)]/26
= [41 ± 89]/26
= 5 or -1.8
since x can not be -ve
=> x = 5
So time taken by larger tap = x = 5 minutes
time taken by smaller tap = x + 3 = 8 minutes
Answer:
5 & 8 minutes
Step-by-step explanation:
Two taps together can fill a tank completely in 40/13 minutes. The smaller tap takes 3 minutes more than the bigger tap to fill the tank. How much time does each tap take to fill the tank completely?
Lat Say larger Tap take x minutes to fill tank
tank filled in 1 minute = 1/x
Smaller Tap will take x+3 minutes to fill tank
tank filled in 1 minute = 1/(x+3)
Bot taps together fill in 1 minute = 1/x + 1/(x+3)
= (x + 3 + x)/(x(x+3))
= (2x+3)/(x(x+3))
Tank will be filled in x(x+3) / (2x+3) minutes by both taps together
Two taps together can fill a tank completely in 40/13 minutes.
x(x+3) / (2x+3) = 40/13
=> 13x² + 39x = 80x + 120
=> 13x² -41x - 120 = 0
=> 13x² -65x + 24x - 120 = 0
=> 13x(x-5) + 24(x-5) = 0
=> (13 x + 24)(x-5) = 0
=> x = 5 x = -24/13 not possible as x can not be negative
Larger tap take 5 minutes
Smaller tap take 5+3 = 8 minutes