Question

A large aquarium of water is being filled with a hose. Due to a problem, the sensor does not start working until some time into the filling process. The sensor starts its recording at the time zero minutes. The sensor initially detects the tank has 225 liters of water in it. The hose fills the aquarium at a constant rate of 15 liters per minute. What will the sensor read at the time 5 minutes? Later, someone wants to use the data to find the amount of water at times before the sensor started. What should the sensor have read at the time -7 minutes?

Answer 1

Answer: After 5 minutes, the sensor will read 300 liters.

After -7 minutes, the sensor sensor should have read 120 liters.

Explanation:

Given: Due to a problem, the sensor does not start working until some time into the filling process.

The initial amount of water detected by sensor = 225 litres

Since, the hose fills the aquarium at a constant rate of 15 liters per minute.

Let x be the time , and y be reading of sensor then

`y=225+15x`

Therefore, the sensor reads after 5 minutes, substitute x=5 in the above equation, we get

`y=225+15(5)=300\ liters`

To find the sensor reading at time -7 minutes substitute x=-7 in the above equation, we get

`y=225+15(-7)=120\ liters`

Therefore, the sensor should have read 120 liters at time -7 minutes.