Rate problem

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Ilikemeat321: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jul 24, 2008 7:33 am

by Ilikemeat321 » Wed Aug 13, 2008 5:51 pm

Can some explain this?

Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floor per minute. If they continue traveling at these rates, at which floor will their path cross?

A 19
B 28
C 30
D 32
E 44

I tried using rt=d formula

D = distance between 11th and 51th which is 40 floors

Steve + Joyce will be 57t+63t

57t+63t=40
t=.04

but I'm lost after this.

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Source: Beat The GMAT — Problem Solving | Wed Aug 13, 2008 5:51 pm

sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Wed Aug 13, 2008 7:58 pm

i got the answer as 30.C

i would step up the equation as ..

The floor Steve is on, at any given time:
11 + 57 * t (minutes)

Joyce:

51 - 63 * t (minutes)

When they cross, the two equations will be equal. Therefore,

t = 40 / 120 = 1/3 (min) = 20 seconds.

t = 1/3

if u substitute this in the equation ... u will get 30.

hope it helps...

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Ilikemeat321: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jul 24, 2008 7:33 am

by Ilikemeat321 » Thu Aug 14, 2008 2:55 am

thanks! is there another way doing it? like the using the rt=d formula?

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pepeprepa: Legendary Member; Posts: 661; Joined: Tue Jul 08, 2008 12:58 pm; Location: France; Thanked: 48 times

by pepeprepa » Thu Aug 14, 2008 3:12 am

There are 40 floors between the two guys.
The cumulated speed of both is 120 floors per minute (57+63)
40/120=1/3 of minute or 20 seconds to join each one.

In 20 seconds, Joyce downs 21 floors (63*20/60).
Given he was at the 51th floor, it means they meet at the 51-21 floors, 30 floors

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Ilikemeat321: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jul 24, 2008 7:33 am

Re: Rate problem

by Ilikemeat321 » Thu Aug 14, 2008 5:24 am

Ilikemeat321 wrote:Can some explain this?

Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floor per minute. If they continue traveling at these rates, at which floor will their path cross?

A 19
B 28
C 30
D 32
E 44

I tried using rt=d formula

D = distance between 11th and 51th which is 40 floors

Steve + Joyce will be 57t+63t

57t+63t=40
t=.04

but I'm lost after this.

O boy I just realized I made a mistake, using my forumla I would get T= 1/3 as well, then if I plug in T with each person I would get the floors. Thanks for all the help

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