Prob Logic

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Sher1: Master | Next Rank: 500 Posts; Posts: 116; Joined: Fri Feb 20, 2009 9:26 am; Location: New Jersey; Thanked: 7 times; GMAT Score:660

Prob Logic

by Sher1 » Mon Aug 24, 2009 1:44 pm

A man cycling along the road noticed that every 12 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?

5 minutes
6 minutes
8 minutes
9 minutes
10 minutes

Quote

Source: Beat The GMAT — Problem Solving | Mon Aug 24, 2009 1:44 pm

grockit_jake: GMAT Instructor; Posts: 80; Joined: Wed Aug 12, 2009 8:49 pm; Location: San Francisco, CA; Thanked: 16 times

by grockit_jake » Mon Aug 24, 2009 2:44 pm

Personally I would pick an easy and arbitrary SPEED for the bike. Let's say 60 mph.

If the bike is at mile 12 and meets the buses going in both directions, at mile 16 he will meet the oncoming bus, and at mile 24, he will hit the passing bus. (Assuming the biker is going 60mph.) This means the SPEED of the BUS = 120mph.

Working 4 minutes backwards for the oncoming bus from mile marker 16 @ 120 mph, that will leave the oncoming bus at mile marker 24 @ time = 0. This confirms that each bus is 12 miles behind the one ahead of it. Since we know all the buses travel at 120mph, and that they are 12 miles apart, then they must be 6 minutes apart. (120mph = 2 miles/minute).

Jake Becker
Academic Director
Grockit Test Prep
https://www.grockit.com