Answer:
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,
- Derek adds water to a pool at a rate of 12 gallons per minute and then reduces the rate to 8 gallons per minute.
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
