Two Formula 1 cars leave the starting line at the same time. One car takes 280 seconds to complete one lap ad the other takes 288 seconds. How long after the start will it take for them to meet again at the starting line?
280(n+1) = 288 (n)
280 = 8 n
n = 35
288 * 35 = 10080 seconds or 2.8 hours
To find out when the two cars will meet again at the starting line, we need to determine the time it takes for them to complete a whole number of laps.
First, we need to find the least common multiple (LCM) of the two lap times: 280 seconds and 288 seconds.
To find the LCM, we can factorize the numbers:
280: 2^3 × 5 × 7
288: 2^5 × 3^2
Now, we take the highest power of each prime factor that appears in either number:
LCM = 2^5 × 3^2 × 5 × 7 = 2,240
Therefore, the two cars will meet again at the starting line after 2,240 seconds or 2240/60 = 37 minutes and 20 seconds.
To find out when the two cars will meet again at the starting line, we need to determine the least common multiple (LCM) of their lap times. The LCM is the smallest multiple that both lap times share. Here's how we can find it:
Step 1: Identify the lap times of each car.
Car 1: 280 seconds
Car 2: 288 seconds
Step 2: Find the prime factors of each lap time.
Car 1: 280 = 2^3 * 5 * 7
Car 2: 288 = 2^5 * 3^2
Step 3: Determine the LCM by taking the highest exponent for each prime factor from both lap times.
LCM = 2^5 * 3^2 * 5 * 7 = 2016
So, the two cars will meet again at the starting line after 2016 seconds.