Question

A water tank holds 256 gallons but is leaking at the rate of 3 gallons per week. A second water tank holds 384 gallons and is leaking at a rate of 5 gallons per week.After how many weeks will the amount of water in the two tanks be the same.

Answer 1

Simple....

you have: one is leaking 3 gallons per week and holds 256 gallons; whereas, the other one is leaking 5 gallons per week and holds 384 gallons.

Set up both the equations....

In y=mx+b form--->>>

y=-3x+256

y=-5x+384

To figure out when they will be equal..set the equations equal to each other....(remember to isolate the variable)

-3x+256=-5x+384

-3x+256=-5x+384
      -256        -256

-3x=-5x+128

-3x=-5x+128
+5x+5x

2x=128

x=64

After 64 weeks the amount of water in both tanks will be the same.

Thus, your answer.

Answer 2

Based on the quantity of water in the tanks and the leakage rate, the two tanks will be equal after 64 weeks.

The first tank has 256 gallons and is leaking at 3 gallons per week. Assuming the number of weeks is x, the expression is:

= Water in tank - (Gallons leaking per week x No. of weeks)

= 256 - (3 × x)

= 256 - 3x

The second tank:

= 384 - 5x

To find the number of weeks they would be equal, equate both tanks:

384 - 5x = 256 - 3x

384 - 256 = -3x + 5x

128 = 2x

x = 128 / 2

x = 64 weeks

In conclusion, the tanks would hold the same amount of water in 64 weeks.

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