Question

Write and solve an inequality for the following: 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?

Answer 1

Step 1

Find the unit rate

$\frac{15}{10} \frac{gallons}{minute}= \frac{1.5}{1} \frac{gallons}{minute}$

Step 2

Convert  $\frac{gallons}{minute}$ to $\frac{gallons}{hour}$

we know that

$1\ hour=60\ minutes$

so

$\frac{1.5}{1} \frac{gallons}{minute}=\frac{1.5}{(1/60)} =60*1.5=90\frac{gallons}{hour}$

Step 3

Find the inequality

Let

x--------> the time in hours

$90x < 315$ ------> this is the inequality

Step 4

Solve the inequality

$90x < 315$

Divide by $90$ both sides

$90x/90 < 315/90$

$x < 3.5\ hours$

therefore

the answer is

Hose can be left on before tank overflows less than $3.5\ hours$

Answer 2

Rate of flow of water in the fish tank will be given by:
rate=volume/time
the rate of our tank is 15 gallons every 10 minutes. Thus,
rate=15/10=1.5 gallons/ minute
Therefore time taken for the tank to overflow will be:
time=volume×rate
volume of the tank=315 gallons
rate=1.5 gallons per minute
hence:
time=315×1.5
=472.5 minutes
=7 7/8 hours=7.875 hours