At a speedway, the yellow car completes a lap every 30 seconds and the blue car completes a a lap every 50 seconds. If the cars both start at the same place, how long will it take for the blue car to 'lap' the yellow car?
To determine how long it will take for the blue car to lap the yellow car, we need to find the least common multiple (LCM) of their lap times.
The lap time for the yellow car is 30 seconds.
The lap time for the blue car is 50 seconds.
To find the LCM of 30 and 50, we can list their multiples and identify the smallest common multiple:
Multiples of 30: 30, 60, 90, 120, 150, ...
Multiples of 50: 50, 100, 150, ...
From the lists above, we can see that the smallest common multiple of 30 and 50 is 150.
Therefore, it will take 150 seconds for the blue car to lap the yellow car.
To find out how long it will take for the blue car to lap the yellow car, we need to determine the time it takes for the blue car to travel the same distance as the yellow car.
First, let's find the least common multiple (LCM) of the lap times for the yellow car (30 seconds) and the blue car (50 seconds). The LCM is the smallest number that both lap times divide into evenly.
Let's find the prime factors of each lap time:
- Lap time for yellow car (30 seconds): 2 × 3 × 5
- Lap time for blue car (50 seconds): 2 × 5 × 5
To calculate the LCM, we take the highest power of each prime factor considering both lap times:
- LCM = 2 × 3 × 5 × 5 = 150
Therefore, the blue car and the yellow car will complete a lap at the same time after 150 seconds.
So, it will take 150 seconds for the blue car to lap the yellow car.
lapping means the yellow car passes the blue car
... it has completed one more lap than the blue car
t = time to lap ... in seconds
t / 30 = (t / 50) + 1