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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 am; Location: India; Thanked: 267 times; Followed by:80 members; GMAT Score:760

directly west

by sanju09 » Thu Mar 19, 2009 5:40 am

If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
A. 50 miles
B. 100 miles
C. 500 miles
D. 700 miles
E. 1,000 miles

OA C

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Source: Beat The GMAT — Problem Solving | Thu Mar 19, 2009 5:40 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Thu Mar 19, 2009 5:52 am

Directly north and directly west make the cathti of a right triangle, so the distance you are looking for is the hypotenuse of this triangle.

The one that that travels north travels 2 hours, speed 150 mph. This means the distance from the airport will be 2*150 = 300 miles.

The one that travels west has an average speed of 200 mph, meaning its distance from the airport will be 2*200 = 400 miles.

Distance between the two: sqrt(400^2 + 300^2) = 500 miles.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Aug 06, 2019 4:46 pm

sanju09 wrote:If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?
A. 50 miles
B. 100 miles
C. 500 miles
D. 700 miles
E. 1,000 miles

OA C

The paths of the planes create right triangle, with the distance between them equaling the hypotenuse of the triangle.

The distance of the first plane from the airport at 3:00 PM (2 hours after departure) is 2 x 150 = 300.

The distance of the second plane from the airport at 3:00 PM (2 hours after departure) is 2 x 200 = 400.

Thus, the distance between the two planes is 500, since we have a 300-400-500 right triangle.

Answer: C

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