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Sagot :
Answer:9:24
Step-by-step explanation:
We know that they will meet some time $T$ after 8:00 and that $T$ must be a multiple of 4, 7, and 6. So our job is to find the smallest multiple of those three numbers. Since 4 and 7 share no factors, the first number that is a multiple of both will be $4\cdot7=28$. Next, we must find the smallest multiple of 28 and 6. We can do this in two ways: by listing multiples of 28 until we find one that is a multiple of 6 or by finding what factors of 6 that 28 is missing and multiplying by those factors.
Method 1: The multiples of 28 go 28 (not divisible by 6), 56 (not divisible by 6), 84 (which is divisible by 6!)... So the smallest multiple of 4, 7, and 6 is 84.
Method 2: The factors of 6 are 1,2,3, and 6, so we can write 6 as $2\cdot3$. 28 is divisible by 2 but not by 3, so we must multiply it by 3. We find $28\cdot3=84$ and 84 is therefore the smallest multiple of 4, 7, and 6.
Now we just need to find the time that is 84 minutes after 8:00. Since 9:00 is 60 minutes after 8:00, we just need 24 more minutes after that (since $60+24=84$). The final time is therefore $\boxed{9:24}.$
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