Word problems

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sud21: Master | Next Rank: 500 Posts; Posts: 344; Joined: Sat Nov 12, 2011 3:21 amFollowed by: 2 members; Thanked: 1 times

by sud21 » Sun Sep 20, 2015 12:55 pm

The afternoon before a popular amusement park opens for the season, Shirley has a pass that will let her ride each ride continuously without waiting in line. For each of the four most popular rides, the ride will run for an allotted time, then stop to change passengers (in negligible time) and start again. The Sea Serpent runs every 15 minutes starting at 10am. The Wild Mouse runs every 30 minutes starting at 11am. The Raptor runs every 40 minutes starting at noon. And the Mantis runs every 45 minutes starting at 11am. Each ride runs continuously and stops only to let its passengers off and immediately begin again. If Shirley is able to get on her first ride starting at 2:00pm and wants to ride all four rides, but needs 10 minutes between rides to move from one to the next, what is the earliest time she could finish riding all four rides?

4:15pm

4:30pm

4:45pm

5:00pm

5:15pm

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Source: Beat The GMAT — Problem Solving | Sun Sep 20, 2015 12:55 pm

Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Thu Sep 24, 2015 10:29 am

Let's start with a time table of the rides. ("Leave" indicates the time that Shirley would be able to get to the next ride, since the wait is 10 minutes.)

Sea Serpent: x:00, x:15, x:30, and x:45
leave: x:10, x:25, x:40, x:55

Wild Mouse: x:00, and x:30
leave: x:10, x:40

Raptor: 2:00, 2:40, 3:20, 4:00
leave: 2:10, 2:50, 3:30, 4:10

Mantis: 2:00, 2:45, 3:30
leave: 2:10, 2:55, 3:40

Since the ride time is 15 + 30 + 40 + 45 = 130 minutes and the transit time between rides is at least 3*10 = 30 minutes, Shirley must be at the park for at least 160 minutes, or 2 hours and 40 minutes, so she must be there until 4:40. This makes me think the answer is 4:45, so I looked for a path that would satisfy that.

Wild Mouse 2:00 to 2:30
Raptor 2:40 to 3:20
Sea Serpent 3:30 to 3:45
Mantis 4:00 to 4:45

so she's done at 4:45, and we're done too!

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