Problem Solving

I can't seem to find a good systematic way of approaching these problems.

Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per min. 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 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A. 19
B. 28
C. 30
D. 32
E. 44

OA: c

Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

A. 9:30
B. 9:00
C. 8:40
D. 7:50
E. 7:00

OA: D

1) First calculate the number of floors between Steve and Joyce

51-11 = 40.

Now total distance between them = 40 floors

Lets say steve rides x floors in time t. For Joyce to meet steve, she should travel (40-x) floors in the same time t, since both start at the same time. We need to find out 11+x.

the equations are

57 x t = x -->1

63 x t = 40-x -->2

63t = 40 - 57t

t = 1/3

x = 19

steve meets joyce at 11+ 19 = 30th floor.

2) Tom's speed S(T) = 30p/hr
Jan'd speed S(J) = 40p/hr

Just as we wrote 2 equations for previous problem, write for this one too.

if t is the time it takes Tom to end up on the some x page, Jan reached that same page in t-40[since she started 40 minutes late], however ended up reaching that same page. t is in minutes.

now since the number of pages they read are same we can have

30 x (t) = 40(t-50)
t = 200 minutes = 3 hr 20 minutes

Time should be 4:30 + 3 hr 20 min = 7:50


Its just a matter of writing down everything in the form of equations.

ahh that makes sense now. Thanks! I couldn't remember how to form an equation while I was taking the practice test.

luckyjoe wrote:I can't seem to find a good systematic way of approaching these problems.

Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per min. 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 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?

A. 19
B. 28
C. 30
D. 32
E. 44

OA: c

Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom starts reading a novel at 4:30, and Jan begins reading an identical copy of the same book at 5:20, at what time will they be reading the same page?

A. 9:30
B. 9:00
C. 8:40
D. 7:50
E. 7:00

Here's the #1 thing to remember for this type of question:

if two objects are travelling in opposite directions, ADD their rates; if two objects are travelling in the same direction, SUBTRACT their rates.

For the first question, the elevators are travelling towards each other, which means they're travelling in OPPOSITE directions (one up, one down).

So, the combined rate is 57 + 60 = 120 floors per minute.

The total distance they need to travel to meet is their separation at time of start, 40 floors.

time = distance/rate = 40/120 = 1/3 of a minute.

Now we can look at either elevator to see what floor it will be on after 1/3 of a minute.

If we chose the bottom one, we get:

d = r*t = 57(1/3) = 19

11th floor + 19 floors = 30th floor.

If we chose the top one, we get:

d = r*t = 63(1/3) = 21

51st floor - 21 floors = 30th floor.

* * *

For the second question, we have a bit of a twist, since they start at different times. The first thing we need to do is equalize the times, i.e. figure out how many pages Tom has read when Jan starts.

Jan starts 50 minutes, or 5/6 of an hour, after Tom. So:

d = r*t
d = 30(5/6) = 25 pages.

In order to catch up, Jan must travel a relative distance of 25 pages. Since Tom and Jan are going in the same direction (they're both reading the book from start to finish), to calculate the "catch up" rate we SUBTRACT the individual rates.

40-30 = 10, which means that every hour Jan catches up by 10 pages.

t = d/r = 25/10 = 2.5 hours.

Since Jan started at 5:20, she'll catch up to Tom at:

5:20 + 2:30 = 7:50.

* * *

Back to the first question, we also could have solved very quickly with ratios.

The ratio of rates is 57:63 = 19:21 (which, not coincidentally, adds up to 40, the total number of floors to travel - the GMAT loves to reward people who pay attention!).

So, the bottom elevator will travel 19 floors in the same time that the top elevator travels 21 floors.

11 + 19 = 30
51 - 21 = 30

so they meet on the 30th floor.