Question

A fish tank can hold at most 315 gallons of water. If a hose is filling the fish tank at a rate of 15 gallons every 10 minutes, how many HOURS can the hose be left on before the tank overflows? Translate the phrase into an inequality.

Answer 1

3 1/2 hours

Step-by-step explanation:

315 / 15 = 21

21 x 10 = 210

210 / 60 = 3.5

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Answer 2

Answer: The inequality is
`315-90x\geq 0`. The hose can be on for less that or equal to
`3(1)/(2)` hours.

Step-by-step explanation:

The capacity of tank is 315 gallons.

Let the hose can on for time (in hours) t.

The hose is filling the fish tank at a rate of 15 gallons every 10 minutes.

10 min = 15 gallons

1 min = 1.5 gallons

Because we know that 1 hour = 60 min,

1 hour = 1.5(60) = 90

Therefore the tank is filling 90 gallon per hour.

The tank filled in t hours is 90t.

Since the capacity of tank is 315 gallons. So 90t is always less than 315.

`90t\leq 315`

`0\leq 315-90t`

It can be written as
`315-90x\geq 0`.

Solve the inequality we get,

`90t\leq 315`

`t\leq 3(1)/(2)`

So the hose can be on for less that or equal to
`3(1)/(2)` hours.