+0  
 
0
53
2
avatar

With both taps turned on, a tank can be filled in 24 minutes. With only one tap on, One of the taps takes twenty minutes longer than the other tap to fill the tank. How long does it take the faster tap to fill the tank by itslef.

 Apr 28, 2020
 #1
avatar+23646 
+1

x = faster tap

(x+20) = slower tap

 

1/x  + 1/(x+20) = 1/24

x + 20 + x = (x^2+20x)/24

48x + 480 = x^2 + 20x

x^2 -28x-480 = 0                        Use quadratic formula to find x = 40 min

 Apr 28, 2020
 #2
avatar+20981 
+1

Let the time of the faster one be "t"

then the time of the slower one is "t + 20".

 

Equation:                                                          [1/t] + [1/(t + 20)]  =  1/24

Multiplying through by  24(t)(t + 20)     --->     [24(t + 20)] + [24t]  =  [t(t + 20)]

                                                                            24t + 480 + 24t  =  t2 + 20t

                                                                                t2 - 28t - 480  =  0

                                                                              (t - 40)(t + 12)  =  0

 

         t = 40 minutes

t + 20  =  60 minutes

 Apr 28, 2020

21 Online Users

avatar