Question

1. log(10^2x - 56) - x = 0

2. Two taps A and B are used to fill up a tank with water. If tap A is used alone to fill up the tank, it takes 25 minutes longer than using tap B alone. If each of tap A and tap B is turned on alone for 20 minutes one by one and then they are turned on together for 10 minutes, the tank will be full.

Find the time taken to fill up the tank for:
a. Tap A
b. Tap B

I'm not sure how to set up the equation.

Answer 1

For 2. you can use an idea similar to rate*time= distance
in this case, rate is how fast the tank is being filled, time is the time needed, and distance is 1 (meaning 1 full tank)

If tap A is used alone to fill up the tank, it takes 25 minutes longer than using tap B

I would let Ta be the time needed to fill the tank at rate Ra
Also, we can say Ra*Ta= 1 and Ra= 1/Ta

From the first statement:
Tb= Ta-25
Rb*Tb= 1 or Rb= 1/Tb or Rb= 1/(Ta-25)


If each of tap A and tap B is turned on alone for 20 minutes one by one and then they are turned on together for 10 minutes, the tank will be full.

This says: Ra*20 + Rb*20 + (Ra+Rb)*10 = 1
first 20 minutes at A's rate, then 20 mins at B's rate, then together for 10 mins will fill the tank

Replace Ra with 1/Ta
Replace Rb with 1/Tb = 1/(Ta-25)
solve for the time Ta to fill the tank at A's rate.

Answer 2

I attempted to work this from above, and in trying to solve a. (Tap A), I came up with two values; 10 and 75. I would assume it may be 75, but don't trust it because of the ambiguity. Has anyone else tried to solve this using @phi instructions?

Answer 3

@radar Because the value 10 would make Ta - 25 a negative number, it should be rejected.

Answer 4

@tyteen4a03, Thanks.

Answer 5

Did you come up with a similar value for Ta?