a water tap a takes 7 minutes more than the tap b for filling up a tank with water the tab a page 16 minutes more than the time taken by both the taps together to fill the tank find the time each each tap alone tank to fill the tank
Answers
a take 28min to filling up a tank with water And b take 21min to filling up a tank with water
Answer:
28 & 21 mins
Step-by-step explanation:
a water tap a takes 7 minutes more than the tap b for filling up a tank with water the tab a page 16 minutes more than the time taken by both the taps together to fill the tank find the time each each tap alone tank to fill the tank
Let say Tap B takes to fill tank = x minutes
Tank filled by Tap B in 1 minute = 1/x
Tap A takes 7 minutes more than the tap B
Tap A will take time to fill tank = x + 7 min
Tank filled by Tap A in 1 minute = 1/ (x + 7)
Tank filled by both taps in 1 minutes = 1/x + 1/(x+7)
= (x + 7 + x) / (x(x+7))
= (2x+7)/(x² + 7x)
Time taken by both tap to fill tank
= (x² + 7x)/(2x+7)
tap A take 16 minutes more than the time taken by both the taps together to fill the tank
x + 7 = (x² + 7x)/(2x+7) + 16
=> x - 9 = (x² + 7x)/(2x+7)
=> 2x² - 18x + 7x - 63 = x² + 7x
=> x² -18x - 63 = 0
=> x² - 21x +3x - 63 = 0
=> x(x-21) + 3(x-21) = 0
=> (x+3) (x-21) = 0
x =21 x = -3 not possible as time can't be negative
Tap B takes to 21 min to fill tank
Tap A takes to 21+7 = 28 min to fill tank