Help with a bus problem

fecoupefe · #1 $Old$ December 4th, 2008, 04:57 PM

The 101 passes John's house every 8 mins. The 103 bus passes it every 12 minues. The two buses last passed by togethre at 9:00am. When is the next time that will happen?

I thought it might be 1pm but could be way off! Thanks for looking.

nzmathman · #2 $Old$ December 4th, 2008, 05:11 PM

The lowest common multiple of 8 and 12 is 24. So the buses will pass together 24 minutes later at 9:24am.

(101 passes at 9:00, 9:08, 9:16, 9:24.....)
(103 passes at 9:00, 9:12, 9:24.....)

Soroban · #3 $Old$ December 4th, 2008, 05:20 PM

Hello, fecoupefe!

Quote:

The 101 passes John's house every 8 minutes.
The 103 bus passes it every 12 minutes.
The two buses last passed by together at 9:00 am.
When is the next time that will happen?

The very worst you can do is make a list . . .

. . $\begin{array}{cccccccccc} \text{101 bus:} & 9\!:\!00 & 9\!:\!08 & 9\!:\!16 & {\color{red}9\!:\!24} & 9\!:\!32 & 9\!:\!40 & 9\!:\!48 & \hdots\\ \text{103 bus:} & 9\!:\!00 & 9\!:\!12 & {\color{red}9\!:\!24} & 9\!:\!36 & 9\!:\!48 & \hdots\end{array}$

They pass together at 9:24 am.

The easier way is to find the Least Common Multiple of 8 and 12: . $\text{LCM}(8,12) \:=\:24$

They will pass together every 24 minutes.

Too fast for me, nzmathman . . .