Final answer:
To determine how long it takes Cody's dad to wash the car by himself, we compare the work rates of Cody alone and when he works with his dad. Cody's dad also takes 6 hours to wash the car alone, as inferred from subtracting Cody's work rate from their combined work rate.
Step-by-step explanation:
The subject of this question is Mathematics, more specifically, it involves working with rates and time. The question can be solved using the concept of work rates, which can be defined by the equation work = rate × time. To find out how long it takes Cody's dad to wash the car by himself, we need to determine his individual work rate.
- Cody takes 6 hours to wash the car, so his work rate is 1/6 car per hour.
- When Cody and his dad work together, they take 3 hours to wash the car, which means their combined work rate is 1/3 car per hour.
To find Cody's dad's individual work rate, we subtract Cody's rate from their combined rate:
Combined rate - Cody's rate = Dad's rate
1/3 - 1/6 = 1/6 (Dad's rate)
Therefore, Cody's dad's work rate is 1/6 car per hour. To find the time it takes for Cody's dad to wash the car, we use the reciprocal of the work rate:
Time = 1 / Work rate
Time = 1 / (1/6)
Time = 6 hours
So, it would take Cody's dad 6 hours to wash the car by himself.