Two taps together can fill a tank completely in 1×1/13 min . the smaller tapp takes 3 min more than the bigger tap to fill the tank . how much does each tap take to fill the tank completely?
Answers
CORRECTION IN THE QUESTION:::::
two taps together can fill a tank completely in 3 1/13 min.
GIVEN:::::
two taps fill the tank in 40/13 min (converted into proper fraction)
small tap takes 3 min more that large tap to fill the tank alone
TO FIND:::::
time taken by two taps separately to fill the tank.
APPLIED CHAPTER::::::
quadratic equations.
HOW TO FIND::::::
let time taken by the large tap to fill be x
then,
time taken by small tap = x +3 ( 3 min more)
now
large tap fills 1/x part of the tank in 1 min
small tap fills 1/x+3 part of the tank in 1 min
ACCORDING TO THE QUESTION,
1/x + 1/x+3 = 13/40 (13/40 is the part of the tank filled in 1min)
2x + 3/x² + 3x = 13/40
13(x² + 3x) = 40(2x + 3)
13x² + 39x = 80x + 120
13x² - 41x - 120 = 0
using quadratic formula,
OR
factoriise if u like
I PREFER QUADRATIC FORMULA..WE GET::::
(13x+24)(x-5) = 0
x = -24/14 OR 5
IGNORE NEGATIVE VALUE
TO GET x = 5
HENCE
TIME TAKEN BY LARGE TAP IS 5 MIN
ANSWER:::::::
TIME TAKEN BY LARGE TAP (x) = 5min
TIME TAKEN BY SMALL TAP(x+3) = 8min
THANKING YOU
Answer:
answer is shown above in the photo
