Nick and Isaiah both run a mile. Nick runs in 8 minutes and Isaiah runs it in 10 minutes. How long would it take Nick to run pass Isaiah for a second time. I think the answer is 16 mintues. The LCM =40
How did you get that first of all?
The chapter was about finding the LCM which in this case is 40. But I thought since the first time around it takes him 8 minutes, then the 2nd time would be 16 minutes. It would take him 5 trips to equal 40 and Isaiah 4 trips. But Nick's time is still beter than Isaiah.
Oh by the way they start at the same time..
Nick's rate is 1/8 mi/min
Isah's rate is 1/10 mi/min
(Time = Distance/rate or Distance = rate x time)
You don't say how long the track is, but we know that if Nick ran n laps, at the first time Isah is passed, Isah would have run n+1 laps
So Nick's time = (n+1)/(1/8) minutes
Isah's time = n/(1/10) minutes.
At the times would be the same for the first passing, so
(n+1)/(1/8) = n/(1/10)
This solves to n = 4
subbing that back into either of their times gives me 40 minutes.
So Nick will pass Isah for the first time in 40 minutes, and the second time obviously in 80 minutes.
(clearly they must be running some type of marathon)
I found the same problem in my son's math homework when he learned LCM. That's maybe why my son used LCM to solve it.
I used similar way to Reiny's.
i.e.
Nick's speed: 1/8.
Isah's speed : 1/10.
When Nick passed Isah for the second time, Nick will run 1 more mile than Isah. so the time should be:
1/(1/8-1/10)=40 minutes.
the author of this problem assumed that he passed him at the same place
To find the time it would take for Nick to pass Isaiah for a second time, we need to find the least common multiple (LCM) of their individual times.
The LCM is the smallest number that is divisible by both 8 and 10. To find the LCM, we can list the multiples of each number until we find a common multiple:
Multiples of 8: 8, 16, 24, 32, 40, ...
Multiples of 10: 10, 20, 30, 40, ...
As we can see, the first common multiple is 40. Therefore, the LCM of 8 and 10 is 40 minutes.
So, for Nick to run past Isaiah for a second time, it would take him 40 minutes, not 16 minutes.