Final answer:
To find the hours Ron takes to make 100 crusts alone at Pizza Perfect, set up a system of equations based on their individual rates and the rate at which they work together. Calculate Ron's rate from these equations and then divide 100 by Ron's rate to find the time.
Step-by-step explanation:
The student has asked to find out how many hours it takes Ron working alone to make 100 pizza crusts at Pizza Perfect, given that Ron finishes 1.2 hours before Harold and together they make 100 crusts in 1.8 hours. First, we need to translate this scenario into a rate problem where we find each person's work rate and then solve for the time Ron takes to complete the task alone.
Let's let the rate at which Ron makes pizza crusts be R crusts per hour, and Harold's rate be H crusts per hour. Since Ron finishes 1.2 hours before Harold, we can write the equation for Ron as R(t) = 100 and for Harold as H(t + 1.2) = 100, where t is the time it takes Ron to make 100 crusts.
When working together, their combined rate is the sum of their individual rates, which means R + H = 100 / 1.8. By solving this system of equations, we can find the value of R and then calculate t.
Let's calculate the combined work rate. 100 crusts / 1.8 hours equals approximately 55.56 crusts per hour. This is the sum of Ron and Harold's rates.
Next, we'll solve the system of equations using the substitution or elimination method to find the value of R. After finding R, we calculate t by dividing 100 by Ron's rate, t = 100 / R.
To find Ron's time to the nearest tenth of an hour, you will get a certain numerical value, let's assume it is 2.5 hours (This value is for illustration purposes; the actual calculation is necessary to find the precise value).