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# how to solve this problem in 2 mins. any easy method?

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how to solve this problem in 2 mins. any easy method? [#permalink]  18 Jul 2011, 13:09
00:00

Difficulty:

5% (low)

Question Stats:

50% (02:10) correct 50% (01:48) wrong based on 6 sessions
X is planning a bus trip across town that involves three buses. Bus 1 travels between house and downtown, and leaves every half-hour starting at 7:20am. X will need to be on Bus 1 for 1 1/5 hours. Bus 2 travels between downtown and uptown every half-hour starting at 7:10am. X will have to be on Bus 2 for 2/3 hour. Lastly, Bus 3 travels between uptown and destination every hour starting at 9 Am. what is the least total amount of time X wmust spend waiting for buses, assuming all buses stay on schedule?

A. 12 mins
B. 18 mins
C. 48 Mins
D. 1 hour 12 mins
E. 1 hour 20 mins
[Reveal] Spoiler: OA

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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  18 Jul 2011, 15:10
Second bus service starts 10 mins earlier than first bus service and both have same frequency (every 30 mins). First bus take 1hr 12 mins.
Thus second bus one can get has waiting time 30 - (10+12)=8 mins
It is same always.
If you write time arrival time for first bus(8:32,9:02,9:32, add 30mins) and departure time for second bus(8:40,9:10,9:40 etc), you will get the same.

Similarly, third bus leaves every hour and service starts exactly on hour clock, a 10 mins early(7:10am and 9am, just mins since buses have frequency of either half or one hour)
Also second bus takes 2 hour 40 mins
Waiting time = 60-(10-40) =10 mins or 10+30=40 mins (since second bus leaves every 30 mins and third every 1hr)

First waiting time is always 8 mins, so take least time 10 mins for second waiting time.
Thus, least waiting time = 8+10 = 18 mins.

It did take more than 2 mins though.
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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  18 Jul 2011, 20:39
I am getting 48 mins as answer and this took 1.32 mins

For bus 2 is it 2/3 hour or the 2 2/3 of the hr, pls clarify.
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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  18 Jul 2011, 22:48
I am getting 48 mins too with 2nd Bus Travel time as 2/3 hour.
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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  18 Jul 2011, 23:06
valencia wrote:
X is planning a bus trip across town that involves three buses. Bus 1 travels between house and downtown, and leaves every half-hour starting at 7:20am. X will need to be on Bus 1 for 1 1/5 hours. Bus 2 travels between downtown and uptown every half-hour starting at 7:10am. X will have to be on Bus 2 for 2/3 hour. Lastly, Bus 3 travels between uptown and destination every hour starting at 9 Am. what is the least total amount of time X wmust spend waiting for buses, assuming all buses stay on schedule?

A. 12 mins
B. 18 mins
C. 48 Mins
D. 1 hour 12 mins
E. 1 hour 20 mins

I go also go with C . 48 mints.. unless 2/3 reads as 7/6 in which case its 18 mints
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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  18 Jul 2011, 23:31
valencia wrote:
X is planning a bus trip across town that involves three buses. Bus 1 travels between house and downtown, and leaves every half-hour starting at 7:20am. X will need to be on Bus 1 for 1 1/5 hours. Bus 2 travels between downtown and uptown every half-hour starting at 7:10am. X will have to be on Bus 2 for 2/3 hour. Lastly, Bus 3 travels between uptown and destination every hour starting at 9 Am. what is the least total amount of time X wmust spend waiting for buses, assuming all buses stay on schedule?

A. 12 mins
B. 18 mins
C. 48 Mins
D. 1 hour 12 mins
E. 1 hour 20 mins

I'd solve it like this:

1 starts at 7:20, 2@7:10, 3@9:00

Start after 9, no risks:

1: 9:20, 9:50, 10:20, 10:50, 11:20, 11:50, 12:20, 12:50, 1:20, 1:50
2: 9:10, 9:40, 10:10, 10:40, 11:10, 11:40, 12:10, 12:40, 1:10, 1:40
3: 9:00, 10:00, 11:00, 12:00, 1:00, 2:00

Test for two start time:

10:20 AND 10:50; One got to be correct

10:20
Travel: 72min
Arrive:11:32
Next:11:40(Wait=8)
Travel: 40min
Arrive:12:20
Next:1:00(Wait=40)
Total=48

10:50
Travel: 72min
Arrive:12:02
Next:12:10(Wait=8)
Travel: 40min
Arrive:12:50
Next:1:00(Wait=10)
Total=18

Ans: "B"
*******************
It will take about 2min to 2.25min max.
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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  19 Jul 2011, 00:39
So, we have to try 2 cenarois then, dint look at the Q stem, it states least wait time, how could one possibly think different.
Fluke - you are an eye opener
Thank You

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Re: how to solve this problem in 2 mins. any easy method? [#permalink]  19 Jul 2011, 04:22
Fluke: Thanks for the explanation!!
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Re: how to solve this problem in 2 mins. any easy method?   [#permalink] 19 Jul 2011, 04:22
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