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.

Answer 1

0+6 L per min
30-9 L per min
so let x represent the time
0+6 times x and
30-9 times x
we want to know what time they will be equal so set them equatl to each other
0+6x=30-9x
6x=30-9x
add 9x to both sides
15x=30
divide both sides by 15
x=2
at 2 mins, they will be equal
find out what that is
subsitute in 0+6x
0+6(2)=0+12=12L

the answers are 2 minutes and 12 liters respectively