Calvin works at the pizza place making pizzas. If he is working alone, he can make an average of 15 3/4 per hour. if he works with his friend Megan, he tends to get distracted, and his rate falls by 1/2 pizza per hour. How many pizzas can Calvin make in an 8-hour shift with Megan? Explain the operations that will be needed to solve this problem, and solve it.
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To solve this problem, we need to follow these steps:
Step 1: Find out how many pizzas Calvin can make in one hour when working alone.
Given that Calvin can make an average of 15 3/4 pizzas per hour when working alone, we can convert this mixed number into an improper fraction. To do that, we multiply the whole number (15) by the denominator (4), then add the numerator (3). This gives us (15 * 4) + 3 = 63/4. So, Calvin can make 63/4 pizzas per hour when working alone.
Step 2: Calculate how many pizzas Calvin can make in one hour with Megan.
Since Calvin's rate falls by 1/2 pizza per hour when working with Megan, we subtract 1/2 from the rate when working alone. So, Calvin can make (63/4 - 1/2) pizzas per hour with Megan.
Step 3: Determine how many pizzas Calvin can make in the entire 8-hour shift.
To find this, we need to multiply the rate per hour with Megan by the number of hours worked. So, (63/4 - 1/2) * 8 gives us the total number of pizzas Calvin can make in the 8-hour shift with Megan.
Now, let's solve it:
Step 1: Convert the mixed number 15 3/4 into an improper fraction: 63/4.
Step 2: Subtract 1/2 from the rate when working alone: 63/4 - 1/2 = (63/4 - 2/4) = 61/4.
Step 3: Multiply the adjusted rate by the number of hours worked: (61/4) * 8 = 61/4 * 8 = 61/2 = 30 1/2.
Therefore, Calvin can make 30 1/2 pizzas in an 8-hour shift with Megan.