OAT Math Question..Help!!

[WSSF]

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Hi everyone,

I am confused on one of the questions from OAT sample test. Can anyone please show me how to solve the question below.

Thanks

Question:
A tank can be filled by a pipe in 30 minutes
and emptied by another pipe in 50 minutes.
How many minutes will it take to fill the tank if
both pipes are open?
A. 45
B. 60
C. 75 (Answer)
D. 80
E. 100

 

[sportsdude00]

Assume the size of the tank is 300 gallons (for easy math).

Take X to be the amount of water IN per minute...
We know that you can fill the tank in 30 minutes, so:
300 gallons/30 minutes= 10 gallons IN per minute

Take Y to be the amount of water OUT per minute...
We know that the tank empties in 50 minutes, so:
300 gallows/50 minutes= 6 gallons OUT per minute

Both holes are open at once, so you have (X-Y), or the amount of water IN-OUT.

You get the equation (X-Y)t=300, with (X-Y) being the difference in water collected, t being the time, and 300 being the tank size. Solve for t and you get 75 minutes.

 

[EyEnStein 07]

haha, these always get people on the SAT...let me show you a quick way
In is 30 minute..Out is 50 minute.

The key is to pay attention to the signs..usually problems like this come in..takes a painter 5 min..another 8 min..how many minutes together. This you have to realize is the difference.

so you proceed like so...

Think of it like this...in 1 minute it fills up 1/30 of a minute "IN"
and in 1 minute it goes out 1/50 of a minute "OUT"

so in and out is a difference (subtraction difference that is)

1/30 - 1/50 = 2/150 in a minute...but its not asking for how much in a minute its asking the total if both pipes of open...simply flip 2/150

and you get 150/2 = 75.

The general rule is... 1/x (+ or -) 1/y = c/z, where c is a value of the differences after you find the lcd.
then you do z/c and you get the answer....

also keep in mind the answer is not going to be negative..so in this case even if you by mistake did 1/50 - 1/30 and got -2/150 -> -150/2 = -75....just take the absolute value...and yes works everytime. (you shouldnt do 1/50 because its less than 1/30..and plus IN should be + out should be -)

 

[WSSF]

Thank you guys.. this really helps 🙂