|
Question 1204130: At 4.45 pm, James, Leo and Noah are at the starting point of a 400-metre circular path. James takes 8 minutes to walk 1 round, Leo takes 180 seconds to run I round while Noah cycles 2 rounds in 3 minutes. Find the time when all three of them will next meet at the starting point.
Found 3 solutions by mananth, greenestamps, ikleyn:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! At 4.45 pm, James, Leo and Noah are at the starting point of a 400-metre circular path.
James takes 8 minutes to walk 1 round,
in 1 minute 1/8 of round
Leo takes 180 seconds to run I round = 3 minutes
1/3 minutes 1 round
while Noah cycles 2 rounds in 3 minutes.
1 round 1.5 minutes
1 minute 2/3 rounds
1/8 , 1/3 , 2/3
Take LCM
LCM =24
So 24 minutes after 4.45 pm they will be at the starting point.
Find the time when all three of them will next meet at the starting point.
Answer by greenestamps(13292)  (Show Source):
You can put this solution on YOUR website!
Leo makes one round every 3 minutes, and Noah makes 2 rounds every three minutes. So Leo and Noah are both again at the starting point every 3 minutes starting at 4:45 pm.
James takes 8 minutes to make one round; Leo and Noah are both back at the starting point every 3 minutes. The least common multiple of those times is 24 minutes.
So 24 minutes after the start is the first time that all three will again be at the starting point.
ANSWER: 24 minutes after the start at 4:45 pm, making it 5:09 pm
Answer by ikleyn(53567)  (Show Source):
You can put this solution on YOUR website! .
At 4.45 pm, James, Leo and Noah are at the starting point of a 400-metre circular path.
James takes 8 minutes to walk 1 round, Leo takes 180 seconds to run I round while Noah cycles 2 rounds in 3 minutes.
Find the time when all three of them will next meet at the starting point.
~~~~~~~~~~~~~~~~~~~~~
James takes 8 minutes to walk 1 round,
Leo takes 3 minutes to run 1 round.
So, if to consider only these two persons, they will be at the starting point simultaneously
next time in LCM(8,3) = 24 minutes and not earlier.
24 is a multiple of 3, so Noah also will be at the starting point together with James and Leo at this time moment.
So, 24 minutes is the closest time when three friends will meet at the staring point.
The clock will display the time 4.45 pm + 24 minutes = 5.09 pm. ANSWER
Solved.
Thus, I solved the problem mentally without using fractions, working with integer numbers, ONLY.
Compare with the solution by @mananth.
|
|
|
| |
