Question

A hose is used to fill up a 1,200 gallon water truck. Water flows form the hose at a constant rate. After 10 minutes, there are 65 gallons of water in the truck. After 15 minutes there are 82 gallons of water in the truck. How long will it take to fill up the truck?

Answer 1

The time it would take to fill up the truck is approximately 344 minutes

Explanation:

The given parameters of the truck are;

The volume of the water truck, V = 1,200 gallon

The rate at which water flows from the hose. m = Constant rate

The volume of water in the truck after t₁ = 10 minutes is V₁ = 65 gallons

The volume of water in the truck after t₂ = 15 minutes is V₂ = 82 gallons

Therefore, the rate at which water flows from the hose to the truck, 'm', is given by the equation for the slope of a straight (constant variation) line, as follows;

`m = (V_2 - V_1)/(t_2 - t_1)`

Therefore, we have;

`m = (82 \, gallons - 65 \, gallons)/(15 \, minutes - 10 \, minutes) = 3.4 \, gallons/minute`

The point and slope form of the straight line equation relationship between the volume in the tank and the time of flow is given as follows;

V - 82 = 3.4 × (t - 15)

Therefore, the slope and intercept form of the equation is given as follows;

V = 3.4·t - 15 × 3.4 + 82 = 3.4·t + 31

∴ V = 3.4·t + 31

When the tank is filled, V = 1,200 gallons, therefore, we have;

1,200 = 3.4·t + 31

3.4·t = 1,200 - 31 = 1,169

t = 1,169/3.4 = 5845/17 = 343.
`\overline{8235294117647058}`

The time it would take to fill up the truck, t = 343.
`\overline{8235294117647058}` minutes ≈ 344 minutes.