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Waiting on Bus Trip

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by nikhilgmat31 » Tue Sep 15, 2015 1:43 am
Shawn is planning a bus trip across town that involves three buses. Bus 1
travels between Shawn’s house and downtown, and it leaves every half-hour
starting at 7:20AM. Shawn will need to be on bus 1 for 1 hour 12 minutes. Bus 2 travels between downtown and uptown every half-hour starting at 7:10 AM. Shawn will need to be on bus 2 for 2/3 hour. Lastly, bus 3 travels between uptown and Shawn’s destination every hour starting at 9AM. Assuming all buses stay on schedule, what is the least amount of time Shawn must spend waiting for
buses?
(A) 12 minutes
(B) 18 minutes
(C) 48 minutes
(D) 1 hour, 12 minutes
(E) 1 hour, 20 minutes
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by prasannakarthik » Tue Sep 15, 2015 2:12 am
If Shawn starts at 7:20, he will reach down town at 8:32 and will have to wait for 8 minutes to board the bus to up-town. On reaching uptown at 11:20, Shawn will have to wait for 40 minutes to board the bus to his destination. Hence, he will wait for 48 minutes if he were to board the bus at 7:20, 8:20, 9:20 etc from his home. If Shawn starts at 7:50, he will reach downtown at 9:02, and will have to wait for 8 minutes to board the bus to up-town at 10:10 and will reach at 12:50. He will further have to wait for 10 minutes to board the bus at 1:00, hence waiting for a total of 18 minutes. The least amount of waiting time is 18 minutes.
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