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Bus B leaves on monday at 3pm and every 10 hours after. Bus

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Bus B leaves on monday at 3pm and every 10 hours after. Bus [#permalink] New post 30 Oct 2006, 07:57
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Bus B leaves on monday at 3pm and every 10 hours after. Bus C leaves on monday at 4pm and every 15 hours after. On what day do the 2 buses leave at the same time?

... i find that i spend an awful lot of time on questions like this bec i list down the departure times one by one. is there a formula to use for such problems? thanks.
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 [#permalink] New post 30 Oct 2006, 11:47
Well, if listing down the various departure times takes too much time, I guess you could always convert it into an equation. Not entirely sure it's worth the extra effort though.

The example you've given doesn't actually seem to work out I'm afraid since both Bus B and Bus C start repeating their schedules after 4 departures and 6 departures respectively, but let's say that:

Bus B leaves at 3pm on Monday and every nine hours after. Bus C leaves at 4pm on Monday and every ten hours after.

Well, if we set 0 hour as Monday midnight,

Bus B's sched is 15+9B
Bus C's sched is 16+10C

Equating the two:
15 + 9B = 16 + 10C
9B - 10C = 16 - 15 = 1

We can see that we'll first get equivalency by the time B hits it's 9th departure and C hits its 8th departure, or at 15 + 9(9) = 96 hours.

Translating back, that gives us 96/24 = 4 full days after 0 hour, or midnight Friday.

If that strikes you as being easier and faster than just writing out the departure times, you're welcome to it....
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 [#permalink] New post 31 Oct 2006, 06:19
Hi stoneape, just a question...

In the last portion of your computation where....

----------
Equating the two:
15 + 9B = 16 + 10C
9B - 10C = 16 - 15 = 1

We can see that we'll first get equivalency by the time B hits it's 9th departure and C hits its 8th departure, or at 15 + 9(9) = 96 hours.
----------

where did you get 8 for C?

... and the OA of this question is actually "none, the buses never leave at the same time"
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 [#permalink] New post 31 Oct 2006, 07:18
I believe the trick here is to use military time format (24 hour format).
Bus B: 15 + 10B
Bus C: 16 + 15C
Since we want to know when busses leave at the same time, we get
15 + 10B = 16 + 15C
or
10B = 15C + 1
We also know that B and C are integers, since busses leave exactly at xx:00. So in the left part we have 10, 20, 30, … In the right 16, 31, 46, 61 Looking at the pattern, we can conclude that there is no integer B & C that satisfy this equation.
  [#permalink] 31 Oct 2006, 07:18
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