Why is it that the below has t as the time they both walk and t+x = time Bob walks while t+1/2 is the time Wendy walks. Shouldn't the time for Bob just be t? Is the x for the extra time it takes due to leaving from work...it seems like Bob is walking from home too since its "3 miles from their home."
Bob and Wendy planned to walk from their home to a restaurant for dinner together. However, Bob was delayed at work, and Wendy left for the restaurant before Bob did. If the restaurant is 3 miles from their home and Bob left for the restaurant a half-hour after Wendy did, how long did Wendy have to wait for Bob at the restaurant?
(1) Wendy walked at a constant pace of 4 miles per hour
(2) Bob walked at a constant pace of 1 mile per hour faster than Wendy.
Answer
For this problem we can set up an RTD (rate x time = distance) chart for Bob and Wendy. The difficulty is that Bob and Wendy will be traveling the same distance "” it is the amount of time that each will be traveling is unknown.
One way that we can get around this problem is by assigning two different variables for time: one for the amount of time that they are both walking (let's say t), and a second for the amount of time that only Bob is walking (in other words, for the amount of time that Wendy is waiting.) Let's call that variable x. The question, rephrased, is "What is x?" In addition, we may want to "link" Bob and Wendy's rates to see whether the difference in the rates is sufficient. To do that, instead of assigning variables for Bob and Wendy's rates separately, we should assign a variable for Wendy's rate (rw) and a second variable for the difference between Bob and Wendy's rates (y). Bob's rate is then rw + y:
Bob Wendy
R rw + y rw
T t + x t + 1/2
D 3 3
Since rate x time = distance, we have:
(rw + y)(t + x) = 3
rw(t+1/2) = 3
Since they are traveling the same distance, we can set up the equations equal to each other and solve for x.
(rw + y)(t + x) = rw(t+1/2)
rwt + yt + xy + rwx = rwt + 1/2rw
yt + xy + rwx = 1/2rw
x(y + rw) = 1/2rw - yt
x = (1/2rw - t)/(rw + y)
Indeed the difference in rates is not sufficient. Therefore the question can be expressed/rephrased as follows:
What are Wendy's rate and the difference between Bob and Wendy's rate? (Or alternately, what are Bob and Wendy's individual rates?) Note that we can calculate t whenever we know Wendy's rate.
(1) INSUFFICIENT: This statement does not tell us anything about Bob's speed.
(2) INSUFFICIENT: As we saw earlier, knowing the difference between the rates is insufficient. We need to know both of Bob's and Wendy's rates.
(1) and (2) SUFFICIENT: Based on the formula above, x = [1/2(4) - 1·t]/[4 + 1] = (2 - t)/5
But since rw(t+1/2) = 3 and rw = 4, we know that t = 1/4. Therefore x = (2 - 1/4)/5 = 7/20 hours, or 21 minutes.
The correct answer is C.
GMAT Forum
7 postsPage 1 of 1
- JK
Bob and Wendy planned to walk from their home
adding the correct subject to the subject line
- GS
Complicated, help please!
I got the correct answer for this question but through different calculation. I am trying to understand this calculation: (It is very confusing, could someone assist me please? :( Thanks.)
Bob Wendy
R rw + y rw
T t + x t + 1/2
D 3 3
Since rate x time = distance, we have:
(rw + y)(t + x) = 3
rw(t+1/2) = 3
Since they are traveling the same distance, we can set up the equations equal to each other and solve for x.
(rw + y)(t + x) = rw(t+1/2)
rwt + yt + xy + rwx = rwt + 1/2rw
yt + xy + rwx = 1/2rw
x(y + rw) = 1/2rw - yt
x = (1/2rw - t)/(rw + y)
Bob Wendy
R rw + y rw
T t + x t + 1/2
D 3 3
Since rate x time = distance, we have:
(rw + y)(t + x) = 3
rw(t+1/2) = 3
Since they are traveling the same distance, we can set up the equations equal to each other and solve for x.
(rw + y)(t + x) = rw(t+1/2)
rwt + yt + xy + rwx = rwt + 1/2rw
yt + xy + rwx = 1/2rw
x(y + rw) = 1/2rw - yt
x = (1/2rw - t)/(rw + y)
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
here's one very cool insight into this problem:
this is a data sufficiency problem. therefore, it doesn't matter if we ignore the half-hour difference between bob's and wendy's start times, because that doesn't affect the sufficiency of the data.
the only effect of ignoring the half-hour difference is to subtract one half-hour from the answer to the problem. therefore, if a statement is sufficient, it will still be sufficient, and, if it's insufficient, it will still be insufficient.
therefore, we can rephrase the problem statement to say that the two of them left for the restaurant at the same time.
in this case, the question is just 'what's the difference in times between bob and wendy?'
statement (1)
insufficient, because this statement contains no information whatsoever about bob's time.
statement (2)
try plugging in different rates, to see whether the answer is constant (and therefore sufficient):
wendy rate = 1 mph, bob rate = 2 mph: wendy takes 3 hours; bob takes 1.5 hours; difference = 1.5 hours
wendy rate = 2 mph, bob rate = 3 mph: wendy takes 1.5 hours; bob takes 1 hour; difference = 0.5 hours
insufficient
(1) and (2) together:
sufficient, because we'll have both rates and will therefore be able to calculate both times.
ans = c
this is a data sufficiency problem. therefore, it doesn't matter if we ignore the half-hour difference between bob's and wendy's start times, because that doesn't affect the sufficiency of the data.
the only effect of ignoring the half-hour difference is to subtract one half-hour from the answer to the problem. therefore, if a statement is sufficient, it will still be sufficient, and, if it's insufficient, it will still be insufficient.
therefore, we can rephrase the problem statement to say that the two of them left for the restaurant at the same time.
in this case, the question is just 'what's the difference in times between bob and wendy?'
statement (1)
insufficient, because this statement contains no information whatsoever about bob's time.
statement (2)
try plugging in different rates, to see whether the answer is constant (and therefore sufficient):
wendy rate = 1 mph, bob rate = 2 mph: wendy takes 3 hours; bob takes 1.5 hours; difference = 1.5 hours
wendy rate = 2 mph, bob rate = 3 mph: wendy takes 1.5 hours; bob takes 1 hour; difference = 0.5 hours
insufficient
(1) and (2) together:
sufficient, because we'll have both rates and will therefore be able to calculate both times.
ans = c
7 posts Page 1 of 1