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by gmattesttaker2 » Mon May 13, 2013 3:43 pm
Hello,

This is from OG 13. Can you please assist with this:

While on a straight road, car X and car Y are traveling at different constant rates. If car X is now 1 mile ahead of car Y, how many minutes from now will car X be 2 miles ahead of car Y ?

(1) Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.

(2) 3 minutes ago car X was 1/2 mile ahead of car Y.


My approach was as follows:

Rates of Car X and Car Y are different, say r1 and r2.

Currently (Time t1) Car X is 1 mile ahead of Car Y
Let t2 be the time at which Car X is 2 miles ahead of Car Y.

So, t2 - t1 = ?


Currently,

R x T = D

X: r1 x t1 = d + 1

Y: r2 x t1 = d


1) r1 = 50 and r2 = 40 (Given)

So, 50 x t1 = d + 1
and 40 x t1 = d

=> 50t1 = 40t1 + 1
=> t1 = 0.1 hours


Also, 50 x t2 = d + 2
and 40 x t2 = d

=> 50t2 = 40t2 + 2
=> t2 = 0.2 hours

So, t2 - t1 = 0.2 - 0.1 = 0.1 hours i.e. 6 mins


2) 3 mins (0.05 hours) ago Car X was 0.5 miles ahead of Car Y

R x T = D

X: r1 t1 - 0.05 d + 0.5
Y: r2 t1 - 0.05 d


However, I am stuck at this point. Can you please assist? Thanks a lot.

Best Regards,
Sri
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by srcc25anu » Mon May 13, 2013 5:47 pm
3 mins (0.05 hours) ago Car X was 0.5 miles ahead of Car Y
St2: 3 mins ago, car X was 1/2 mile ahead of car Y. NOW car X is 1 mile ahead. That means it took another 3 mins for the car to drive until this point where it is 1 mile ahead of car Y.
Total in 6 mins it gained 1 mile.
so in another 6 mins, it will gain another 1 mile (i.e. a total of 2 miles from Car Y)
Hence Sufficient

ST1 is also sufficient. It states Car X gains 10 miles/ hr over Car Y. So it must be gaining 1 mile in 6 mins. It will gain 2 miles in 12 mins. SUFFICIENT.

Hence D
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by Brent@GMATPrepNow » Tue May 14, 2013 6:08 am
gmattesttaker2 wrote:
While on a straight road, car X and car Y are traveling at different constant rates. If car X is now 1 mile ahead of car Y, how many minutes from now will car X be 2 miles ahead of car Y ?

(1) Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.

(2) 3 minutes ago car X was 1/2 mile ahead of car Y.
Hi Sri,

You're doing much more work than is necessary. Don't forget, the key goal here is to determine whether or not you have sufficient information to answer the target question. You need not actually answer the target question.

Target question: How many minutes from now will car X be 2 miles ahead of car Y?

Given: Car X is now 1 mile ahead of car Y

Statement 1: Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per hour.
Notice that we could easily duplicate this scenario in real life.
Start with Car X 1 mile ahead of car Y (given info)
Have Car X drive at 50 mph and car Y at 40mph.
Use a stopwatch to time how long it takes for Car X to be 2 miles ahead of Y.
As you can see, we have enough information to answer the target question
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: 3 minutes ago car X was 1/2 mile ahead of car Y.
If car X is presently 1 mile ahead, we can see that car X gains 1/2 mile every 3 minutes.
At that rate, car X will gain another 1 mile in 6 minutes.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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