Speed question - NYC to Lake House - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

Speed question - NYC to Lake House

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sal_xcool: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Apr 07, 2009 1:00 pm

by sal_xcool » Thu Feb 24, 2011 9:38 pm

Andrew rides his bike at 15 miles per hour, and it takes him 5 hours to ride from New York City to his lake house.
Andrew's wife, Andrea, leaves New York at the same time, and drives on the same road to the lake house at an
average speed of 50 miles per hour. Thirty minutes after arriving at the lake house, Andrea realizes she forgot
her computer, and begins to drive back to New York. How long after leaving the lake house will she pass her
husband, Andrew, on the road?

A. 1/3 of an hour
B. 5/13 of an hour
C. 1/2 of an hour
D. 9/13 of an hour
E. 19/26 of an hour

OA D

Ok, I have 1:30 mins max to solve this question??
Anybody has developed a proven technique for solving the speed/rate questions? what's the best strategy to tackle these type of problems?

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Source: Beat The GMAT — Problem Solving | Thu Feb 24, 2011 9:38 pm

Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pmFollowed by: 17 members; Location: New York City; Thanked: 76 times; GMAT Score:770

by Rich@VeritasPrep » Thu Feb 24, 2011 9:51 pm

Hey sal_xcool,

First of all, the average time per question is more like 2 minutes, so no need to cut yourself off at 1:30! Also, keep in mind that 2 minutes is an AVERAGE. There are going to be some easier problems that you might solve in less than a minute, and some more difficult ones that take you closer to 3 minutes. Therefore, saying you have a specific amount of time to solve any one given question doesn't really make sense. And it puts unneeded pressure on yourself!!

Hope this helps.

Rich

Rich Zwelling
GMAT Instructor, Veritas Prep

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Feb 24, 2011 9:54 pm

sal_xcool wrote:Andrew rides his bike at 15 miles per hour, and it takes him 5 hours to ride from New York City to his lake house.
Andrew's wife, Andrea, leaves New York at the same time, and drives on the same road to the lake house at an
average speed of 50 miles per hour. Thirty minutes after arriving at the lake house, Andrea realizes she forgot
her computer, and begins to drive back to New York. How long after leaving the lake house will she pass her
husband, Andrew, on the road?

A. 1/3 of an hour
B. 5/13 of an hour
C. 1/2 of an hour
D. 9/13 of an hour
E. 19/26 of an hour

OA D

Ok, I have 1:30 mins max to solve this question??
Anybody has developed a proven technique for solving the speed/rate questions? what's the best strategy to tackle these type of problems?

Since Andrew rides at 15mph for 5 hours, d = r*t = 15*5 = 75 miles.
Time for Andrea to arrive at the lake house = d/r = 75/50 = 3/2 hours.
30 minutes later = 2 hours total.
So when Andrea leaves the lake house, Andrew has traveled r*t = 15*2 = 30 miles.
Thus, distance remaining between Andrew and the lake house = 75-30 = 45 miles.
Combined rate for Andrew and Andrea as they travel toward each other = 15+50 = 65 miles per hour. (We combine their rates because they are working together to cover the distance between them, and when people work together, we add their rates.)
Time for Andrew and Andrea to travel 45 miles = d/r = 45/65 = 9/13 hours.

The correct answer is D.

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sal_xcool: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Tue Apr 07, 2009 1:00 pm

by sal_xcool » Thu Feb 24, 2011 10:20 pm

GMATGuruNY wrote:
sal_xcool wrote:Andrew rides his bike at 15 miles per hour, and it takes him 5 hours to ride from New York City to his lake house.
Andrew's wife, Andrea, leaves New York at the same time, and drives on the same road to the lake house at an
average speed of 50 miles per hour. Thirty minutes after arriving at the lake house, Andrea realizes she forgot
her computer, and begins to drive back to New York. How long after leaving the lake house will she pass her
husband, Andrew, on the road?

A. 1/3 of an hour
B. 5/13 of an hour
C. 1/2 of an hour
D. 9/13 of an hour
E. 19/26 of an hour

OA D

Ok, I have 1:30 mins max to solve this question??
Anybody has developed a proven technique for solving the speed/rate questions? what's the best strategy to tackle these type of problems?
Since Andrew rides at 15mph for 5 hours, d = r*t = 15*5 = 75 miles.
Time for Andrea to arrive at the lake house = d/r = 75/50 = 3/2 hours.
30 minutes later = 2 hours total.
So when Andrea leaves the lake house, Andrew has traveled r*t = 15*2 = 30 miles.
Thus, distance remaining between Andrew and the lake house = 75-30 = 45 miles.
Combined rate for Andrew and Andrea as they travel toward each other = 15+50 = 65 miles per hour. (We combine their rates because they are working together to cover the distance between them, and when people work together, we add their rates.)
Time for Andrew and Andrea to travel 45 miles = d/r = 45/65 = 9/13 hours.

The correct answer is D.

Thank you for your awesome explanation

it' def. helps me out.
I didn't see that I could add the speeds. Can you give me example where you can't combine the speeds or rates?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Feb 25, 2011 8:24 pm

sal_xcool wrote: I didn't see that I could add the speeds. Can you give me example where you can't combine the speeds or rates?

Here's the general rule for multiple travelling objects:

if two objects are moving in OPPOSITE directions, ADD the speeds; and

if two objects are moving in the SAME direction, SUBTRACT the speeds.

(Opposite = directly towards each other or directly away from each other.)

This rule applies to all rates, not just speed; for example, on the GMAT we've seen questions involving 2 people reading the same book that ask when the second person will be on the same page as the first person - since they're reading in the same direction (start to finish), you subtract their rates to come up with the "catch up" rate.

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ankur.agrawal: Master | Next Rank: 500 Posts; Posts: 261; Joined: Wed Mar 31, 2010 8:37 pmFollowed by: 3 members; Location: Varanasi; Thanked: 11 times

by ankur.agrawal » Fri Feb 25, 2011 10:05 pm

I think there is a flaw in the question.

No where in the question it is mentioned that Andrea drives back to Newyork at the same average speed.

How do we assume that ?

sal_xcool wrote:Andrew rides his bike at 15 miles per hour, and it takes him 5 hours to ride from New York City to his lake house.
Andrew's wife, Andrea, leaves New York at the same time, and drives on the same road to the lake house at an
average speed of 50 miles per hour. Thirty minutes after arriving at the lake house, Andrea realizes she forgot
her computer, and begins to drive back to New York. How long after leaving the lake house will she pass her
husband, Andrew, on the road?

A. 1/3 of an hour
B. 5/13 of an hour
C. 1/2 of an hour
D. 9/13 of an hour
E. 19/26 of an hour

OA D

Ok, I have 1:30 mins max to solve this question??
Anybody has developed a proven technique for solving the speed/rate questions? what's the best strategy to tackle these type of problems?

Like this post

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

by sanju09 » Sat Feb 26, 2011 12:41 am

sal_xcool wrote:Andrew rides his bike at 15 miles per hour, and it takes him 5 hours to ride from New York City to his lake house.
Andrew's wife, Andrea, leaves New York at the same time, and drives on the same road to the lake house at an
average speed of 50 miles per hour. Thirty minutes after arriving at the lake house, Andrea realizes she forgot
her computer, and begins to drive back to New York. How long after leaving the lake house will she pass her
husband, Andrew, on the road?

A. 1/3 of an hour
B. 5/13 of an hour
C. 1/2 of an hour
D. 9/13 of an hour
E. 19/26 of an hour

OA D

Ok, I have 1:30 mins max to solve this question??
Anybody has developed a proven technique for solving the speed/rate questions? what's the best strategy to tackle these type of problems?

The distance from New York City to the lake house = 15 Ã— 5 = 75 miles. These 75 miles could be covered by Andrea in 1.5 hours. Thirty minutes after Andrea arriving at the lake house, Andrew would have covered 15 Ã— 2 = 30 miles. Hence the moment Andrea begins to drive back to New York, the couple are 75 - 30 = 45 miles apart from each other (here is where I smell little ambiguity in the wordings, it should have been worded like "Andrea realizes she forgot her computer, and begins to drive back with her same average speed to New York", but I am taking it for granted here), which is meant to be covered by the two with the relative speed of 15 + 50 = 65 mph, and hence it would take Andrea [spoiler]45/65 = 9/13 hours[/spoiler] to pass her husband, Andrew, on the road.

[spoiler]D[/spoiler]

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