Stuck with language part of 3 work and rate problems.

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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 amFollowed by: 5 members; Location: Delhi; Thanked: 1 times

by alltimeacheiver » Sun Apr 17, 2011 2:31 am

[size=0]Ques 1 An hour after jane started walking from x to y , a distance of 45 miles. Bob started walking from y to x . If Jane travels a 3mph and bob travels at 4 mph then how much distance had bob travelled when they meet?

Ques 2 Bob can read 30 pages and jane can read 40 pages in an hour, Bob starts with novel at 4.30 pm and jane starts with same novel at 5.20 pm , then at what time they will be reading the same page.

ques3 Bob enters a lift on 21st floor , which is goingup @ 57 floors/min. At the same time jane enters another lift on 61st floor which is going down @ 63 floors/mon . At what floor will they meet

I dont have ans choices with me . Gmat guns help me out[/size]

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Source: Beat The GMAT — Problem Solving | Sun Apr 17, 2011 2:31 am

Geva@EconomistGMAT: GMAT Instructor; Posts: 905; Joined: Sun Sep 12, 2010 1:38 amFollowed by: 123 members; Thanked: 378 times; GMAT Score:760

by Geva@EconomistGMAT » Sun Apr 17, 2011 3:26 am

with combined rate questions, the main problem is to identify which of two possible treatments particular problem requires:

1) add the rates (if the two objects are working together to finish a task, such as building a wall, emptying a pool, or, as is the case in two of the problem below, closing the "gap" between them by walking towards each other at their respective rates.

Or

2) Subtract the rates (if the two objects are working against each other to finish a task, such as one builds while another destroys, one pipe fills the pool while the other drains it, or, as with Q2, one side "runs away" while the other is trying to catch up.

alltimeacheiver wrote:[size=0]Ques 1 An hour after jane started walking from x to y , a distance of 45 miles. Bob started walking from y to x . If Jane travels a 3mph and bob travels at 4 mph then how much distance had bob travelled when they meet?

split into two phases:
phase 1: Jane walks alone for 1 hour at a rate of 3 mph. She walks a total distance of 3 miles, and is now only 42 miles awauy from Bob.

Phase 2: Jane and bob work together at a combined rate of 4+3=7 mph to close the distance of 42 miles between them. This takes them 42/7=6 hours to do, in which Bob will travel 4mph*6hours = 24 miles.

Ques 2 Bob can read 30 pages and jane can read 40 pages in an hour, Bob starts with novel at 4.30 pm and jane starts with same novel at 5.20 pm , then at what time they will be reading the same page.

Again, two phases:
Phase 1: bob reads alone for 50 minutes at a rate of 30 pages an hour: he reads 50/60 * 30 = 25 pages.
Phase 2: Jane starts to read the novel alongside bob. Bob has a 25 page head start, and we're looking for the time it takes Jane to overtake him and read the same page. Every hour that passes, Jane reads 40 pages, but Bob also reads 30 more pages: Jane's "catchup" speed is only 40-30 = 10 pages an hour: At this combined rate (the difference between the rates, since Jane is trying to catch up with a "fleeing" Bob), she will take 25/10 = 2.5 hours to catch up with Bob.

ques3 Bob enters a lift on 21st floor , which is goingup @ 57 floors/min. At the same time jane enters another lift on 61st floor which is going down @ 63 floors/mon . At what floor will they meet

Jane and Bob are working together to close the gap between them, so we add the rates: Toegether, they cover 57+63 = 120 floors ever minute, so the 40 floors between 21st and 61st should take them 40/120 = 1/3 a minute to finish, 20 seconds. In those 20 seconds, Bob will travel 20/60 * 57 floors = 57/3 = 19 floors, (while Jane travels 63/3 = 21 floors down from 61), so they will meet at floor 40.

I dont have ans choices with me . Gmat guns help me out[/size]

Last edited by Geva@EconomistGMAT on Sun Apr 17, 2011 3:33 am, edited 1 time in total.

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Sun Apr 17, 2011 3:28 am

Question 1: Distance btw X and Y = 45miles
Jane travelled for 1 hour at a rate of 3miles/ hour = 3miles
Effective distance btw Jane and Bob = 42 Miles
Relative speed btw jane and bob = 3+ 4 = 7miles/hour
42/7 = 6hours
Now in 6 hours Bob travels = 6*4 = 24
in 6 hours Jane travels= 6*3 = 18

So Ans is 24

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

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HSPA: Legendary Member; Posts: 1101; Joined: Fri Jan 28, 2011 7:26 amFollowed by: 13 members; Thanked: 47 times; GMAT Score:640

by HSPA » Sun Apr 17, 2011 3:38 am

Question 2:Bob has a head start = 50/60*30 = 25page
Now lets us observe what is happening on a hourly basis
At 6.20: Bob read 25+30 = 55
Jane read 0+40 = 40
At 7.20: bob read 55+30 = 85
Jane read 40+40 = 80
Now let us consider half hourly from here
At 7.50: bob read 85+15 = 100
Jane read 80+20 = 100 {So they meet at 100th page at 7.50 hours}

First take: 640 (50M, 27V) - RC needs 300% improvement
Second take: coming soon..
Regards,
HSPA.

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