Runner A speed 1km/hour
Runner B speed 2km/hour
They start of at the same point at the oval.In a lap that is 500m, how many times will they meet at the starting point after 10 hours.
I managed to get the LCM for runner A,B using the time taken to complete 1 lap
A=1/2 hrs, B=1/4 hours
=>LCM is 1/2 hrs
In 10 hrs would they have meet 10/(1/2)=20 times at the starting point?
I was told that it will be 19 times,but not sure why!thanks for your help
Hmmm. Looks like 20 to me, too. There aren't any fractional laps to worry about.
To determine how many times Runner A and Runner B will meet at the starting point, we need to find the number of laps each runner completes in 10 hours and see how many times their lap counts coincide.
First, let's determine the number of laps Runner A completes in 10 hours:
Runner A's speed is 1 km/hour, so in one hour, Runner A completes 1 lap.
Therefore, in 10 hours, Runner A completes 10 laps.
Next, let's determine the number of laps Runner B completes in 10 hours:
Runner B's speed is 2 km/hour, so in one hour, Runner B completes 2 laps.
Therefore, in 10 hours, Runner B completes 20 laps.
Now, we need to find the number of times their lap counts coincide or the number of common multiples of 10 and 20.
To do this, we need to find the LCM (Least Common Multiple) of 10 and 20.
The LCM of 10 and 20 is the smallest number that is divisible by both 10 and 20 without leaving a remainder.
To find the LCM, we can list the multiples of both numbers until we find a common one.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...
From the list above, we see that the smallest common multiple of 10 and 20 is 20.
Therefore, Runner A and Runner B will meet at the starting point after every 20 laps.
Since Runner B completes 20 laps in 10 hours, they will meet at the starting point 19 times (one less than the total number of laps completed by Runner B).
So, the correct answer is 19 times.