speed distance prob

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quantskillsgmat: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Fri Apr 23, 2010 1:14 amFollowed by: 1 member; Thanked: 1 times

by quantskillsgmat » Mon Aug 22, 2011 3:09 am

A and B starts moving towards each other from newyork and chicago along a straight line with constant speeds.After meeting in midway A reaches chicago in 9 hrs and B newyork in 16 hrs.fied ratio of their speeds.
4:3
3:4
5:4
4:5
1:2

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Source: Beat The GMAT — Problem Solving | Mon Aug 22, 2011 3:09 am

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 » Mon Aug 22, 2011 3:47 am

quantskillsgmat wrote:A and B starts moving towards each other from newyork and chicago along a straight line with constant speeds.After meeting in midway A reaches chicago in 9 hrs and B newyork in 16 hrs.fied ratio of their speeds.
4:3
3:4
5:4
4:5
1:2

We can plug in the answers, which represent the ratio of A's rate to B's rate.

After A and B meet, A takes less time to finish traveling than B, so A is moving at a faster rate.
Eliminate B, D and E.

Answer choice A: 4:3.
Let A's rate = 4 miles per hour and B's rate = 3 miles per hour.
When elements travel toward each other, we combine their rates, since the elements are working together to cover the distance between them.
Combined rate for A and B = 4+3 = 7 miles per hour.

Let d = 84 miles (the LCM of 4, 3 and 7).
Time for A and B to meet = d/(combined rate) = 84/7 = 12 hours.

In 12 hours, distance traveled by A = r*t = 4*12 = 48 miles.
Remaining distance for A = 84-48 = 36 miles.
Time for A to finish traveling = d/r = 36/4 = 9 hours.

In 12 hours, distance traveled by B = r*t = 3*12 = 36 miles.
Remaining distance for B = 84-36 = 48 miles.
Time for B to finish traveling = d/r = 48/3 = 16 hours.
Success!

The correct answer is A.

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quantskillsgmat: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Fri Apr 23, 2010 1:14 amFollowed by: 1 member; Thanked: 1 times

by quantskillsgmat » Tue Aug 23, 2011 10:14 pm

this is nice approach but i want some mathemtical approach nt plug in.
can anyone help me.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Aug 23, 2011 10:29 pm

quantskillsgmat wrote:A and B starts moving towards each other from newyork and chicago along a straight line with constant speeds.After meeting in midway A reaches chicago in 9 hrs and B newyork in 16 hrs.fied ratio of their speeds.

Say, speed of A and B in km/hrs are a and b respectively and they met after x hours.
Hence, in these x hours A has traveled ax kilometers and B has traveled bx kilometers.

After meeting B has traveled ax kilometers in 16 hours and A has traveled bx kilometers in 9 hours.

But according to our assumptions in 9 hours A will travel 9a kilometers and in 16 hours B will travel 16b kilometers.

Hence, ax = 16b and bx = 9a
Eliminating x from both, 16b/a = 9a/b

Therefore, aÂ²/bÂ² = 16/9 ----> a/b = 4/3

The correct answer is A.

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Wed Aug 24, 2011 12:31 am

My approach is as under,

Let d be the distance between New York and Chicago.

Since, A and B meet midway, the distance travelled when they met each other is d/2.

=> A covers the rest of the distance in 9 hrs => d/2 = 9a
and
B covers the rest of the distance in 16 hrs => d/2 = 16b

Eliminating d, we get a/b = 16/9.

I certainly know that this wrong but can you help me with what am I missing in the approach above?

Regards,

Pranay

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Aug 24, 2011 12:37 am

bubbliiiiiiii wrote:...Since, A and B meet midway, the distance travelled when they met each other is d/2.

You're not missing anything!
You're assuming extra!

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bubbliiiiiiii: Legendary Member; Posts: 979; Joined: Tue Apr 14, 2009 1:38 amFollowed by: 12 members; Location: Hyderabad, India; Thanked: 49 times; GMAT Score:700

by bubbliiiiiiii » Wed Aug 24, 2011 12:39 am

Anurag@Gurome wrote:
bubbliiiiiiii wrote:...Since, A and B meet midway, the distance travelled when they met each other is d/2.
You're not missing anything!
You're assuming extra!

Thanks for clarifying. On self analysis, I reached the same conclusion but just wanted to confirm from a SME.

Regards,

Pranay

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