The taxi leaves every 15 min, the limo leaves every 28 mins, the bus leaves every 40 min, they never take a break from driving from the airport to the hotel
2006-11-28 05:53:00 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
For this you need to figure out the lowest common multiple of the 3 numbers:
LCM(15, 28, 40)
Prime factorization:
15 = 3 x 5
28 = 2 x 2 x 7
40 = 2 x 2 x 2 x 5
Figuring out the maximum number of time each number appears in each factorization you get:
LCM = 2 x 2 x 2 x 3 x 5 x 7 = 840 minutes
840 minutes / 60 minutes/hr = 14 hours
If they were together at 9 a.m. on Monday, they will be together again at 11 p.m. on Monday.
They will then be together every 14 hours after that...
9 a.m. Monday
11 p.m. Monday
1 p.m. Tuesday
3 a.m. Wednesday
5 p.m. Wednesday
7 a.m. Thursday
9 p.m. Thursday
11 a.m. Friday
So the time they will be together on Friday is 11 a.m.
I sure feel sorry for the drivers that get absolutely no breaks at all and have to drive constantly for days on end. :)
2006-11-28 06:00:09 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
I think what you need is the least amount of time in which each of them could complete a whole number of cycles. That is, the least common multiple of 15, 28 and 40. The cycle would sort of "reset" after that amount of time
Factor them: 15 = 5*3, 28 = 2*2*7, 40 = 2*2*2*5. That means the LCM is 5*3*2*2*2*7, or 840. Every 840 minutes, or 14 hours, they leave together. So that would be 11PM Mon., 1 PM Tues., 3 AM Wed., 5 PM Wed., 7 AM Thurs., 9 PM Thurs., 11 AM Fri.
On Friday, they will all leave together at 11:00 AM.
2006-11-28 14:04:33 · answer #2 · answered by Amy F 5 · 0⤊ 0⤋
at 9 am on friday
2006-11-28 13:59:32 · answer #3 · answered by raj 7 · 0⤊ 0⤋
you are missing a variable: the amount of time it takes to do the trip, unless you mean they leave from a dock and instantly another one apears in their place.
2006-11-28 13:56:16 · answer #4 · answered by pito16places 3 · 0⤊ 1⤋