Final answer:
Bob has improved his lap time by 60 seconds per lap. To fulfill an order of 120 omelets in 20 minutes, 10 cooks are needed. The sum of all possible values of x for the equation x² = 25 is 0.
Step-by-step explanation:
Firstly, Bob initially completed 10 laps in 30 minutes, so his lap time was 180 seconds per lap. After improvement, he completed 12 laps in 24 minutes, which equals 120 seconds per lap. To find out how much Bob has improved his lap time in seconds, we subtract the new lap time from the original lap time: 180 seconds - 120 seconds = 60 seconds improvement per lap. Five cooks make 20 omelets in 10 minutes, so they make 2 omelets per minute collectively. Since the order is for 120 omelets in 20 minutes, we need a rate of 120 omelets / 20 minutes = 6 omelets per minute.
To find out how many cooks are needed, we divide the required rate by the rate per cook: 6 omelets/minute ÷ 2 omelets/minute/cook = 3 cooks. However, it's important to remember that we started with five cooks making 20 omelets in 10 minutes, so we need to double their workforce to meet the 20-minute deadline. Thus, 10 cooks are needed to complete the order on time. The equation x² = 25 has two solutions, x = 5 and x = -5. The sum of these values is 5 + (-5) = 0.