Laura fills a bucket with water at a rate of 6 L/min. At the same time, Sarah empties a bucket holding 30 L of water at a rate of 9 L/min. Let l represent the number of liters of water and let t represent time in minutes. The system models this situation.

How many minutes will it take for the buckets to hold equal amounts of water, and how much water will that be?

l = 6t
l = 30 – 9t

It will take ___
minutes for both buckets to hold equal amounts of water. They will each hold ___
liters.

Question

Laura fills a bucket with water at a rate of 6 L/min. At the same time, Sarah empties a bucket holding 30 L of water at a rate of 9 L/min. Let l represent the number of liters of water and let t represent time in minutes. The system models this situation.
 
How many minutes will it take for the buckets to hold equal amounts of water, and how much water will that be?
 
l = 6t
l = 30 – 9t
   
It will take  ___
 minutes for both buckets to hold equal amounts of water. They will each hold  ___
 liters.

vocaloid · Answer

hint: set the equations equal to each other and solve for t

6t = 30 - 9t

know where to go from here?

timinthor · Answer

I think so, im going to try

timinthor · Answer

6t=30-9t
-6t      -6t
30=3t

timinthor · Answer

am i right so far?

vocaloid · Answer

hm, not quite. 

what is -9t - 6t?

timinthor · Answer

Ohhhh i forgot the -9 not a positive 9 my bad, it would be -15t right?

vocaloid · Answer

yeah, so 30 = 15t, which means that t = 2 minutes

vocaloid · Answer

to find the volume, we just use one of the original equations

L = 6t and plug in t = 2

timinthor · Answer

L=6(2) so it would be 12

vocaloid · Answer

yup! that's our final answer. 2 minutes and 12 liters

timinthor · Answer

Okay! Thank you! ill give a medal

timinthor · Answer

Yay! I got 100% on the rest of the test  too! thx!