Consider the original complex figure and the reduction.

what is the scale factor of the reduction?

At the faster rate (12 gallons per minute)

Time = 60t minutes

At the slower rate (8 gallons per minute)

Time = 120 - 60t minute

Step-by-step explanation:

From the question,

From the statement above, it means 12 gallons per minute is the faster rate and

8 gallons per minute is the slower rate

Also,

He adds water to the pool for a total of 2 hours. That is, the total time he spends adding water to the pool at both rates is 2 hours.

From the question, let t be the time in hours that he adds water to the pool at the faster rate. That is,

At the rate of 12 gallons/minute

Time = t hours (Convert to minute)

(NOTE: 1hour = 60 minute)

Time = t × 60 minute

Time = 60t minute

Since the total time spent was 2 hours, then

The time spent when adding water at the rate of 8 gallons / minute will be

Time = 2 - t hours (convert to minute)

Time = (2 - t) × 60 minutes

Time = 120 - 60t minutes

Hence, the algebraic expression for the time he spends adding water to the pool at the faster rate is

Time = 60t minutes

and for the slower rate

Time = 120 - 60t minute