Time taken by car to travel across the bridge

[gmattesttaker2]

Hello,

Can you please assist with the following question from OG 13:

If car X followed car Y across a certain bridge that is 1/2 mile long, how many seconds did it take car X to travel across the bridge?

(1) Car X drove onto the bridge exactly 3 seconds after car Y drove onto the bridge and drove off the bridge exactly 2 seconds after car Y drove off the bridge.
(2) Car Y traveled across the bridge at a constant speed of 30 miles per hour.


Thanks a lot,
Sri

[theCodeToGMAT]

Distance = 0.5 Miles

To find: Time to cross bridge

S=D/T ==> T = D/S = 0.5/S

Statement 1:
Time of Y - Time of X = 1 sec
- 0.5/X + 0.5/Y = 1 (sec)
- 1/x + 1/Y = 2
INSUFFICIENT


Statement 2:
Y = 30 m/h
We have no info about the speed of "X"
INSUFFICIENT

Combining...
1/X = - 2(sec) + 1/30(m/h)
We can convert and solve
SUFFICIENT


Answer[spoiler] {C}[/spoiler]

[GMATGuruNY]

If car X followed car Y across a certain bridge that is 1/2 mile long, how many seconds did it take car X to travel across the bridge?
(1) Car X drove onto the bridge exactly 3 seconds after car Y drove onto the bridge and drove off the bridge exactly 2 seconds after car Y drove off the bridge.
(2) Car Y traveled across the bridge at a constant speed of 30 miles per hour.

Statement 1: Car X drove onto the bridge exactly 3 seconds after car Y drove onto the bridge and drove off the bridge exactly 2 seconds after car Y drove off the bridge.
Case 1:
Car Y starts at 6:00:10 and finishes at 6:00:15.
Total time = 5 seconds.
Car X starts at 6:00:13 (3 seconds after Car Y) and finishes at 6:00:17 (2 seconds after Car Y).
Total time = 4 seconds.

Case 2:
Car Y starts at 6:00:10 and finishes at 6:00:20.
Total time = 10 seconds.
Car X starts at 6:00:13 (3 seconds after Car Y) and finishes at 6:00:22 (2 seconds after Car Y).
Total time = 9 seconds.

The cases above illustrate that Car X's time is ONE SECOND LESS than Car Y's time.
No way to determine Car X's exact time.
INSUFFICIENT.

Statement 2: Car Y traveled across the bridge at a constant speed of 30 miles per hour.
Car Y's time = d/r = (1/2)/(30) = 1/60 hour = 1 minute = 60 seconds.
No way to determine Car X's time.

Statements combined:
Since Car Y's time = 60 seconds, and Car X's time is 1 second less, Car X's time = 60-1 = 59 seconds.
SUFFICIENT.

The correct answer is C.

[Divya Ann Chacko]

Actually i was looking for the explanation to this question. Excellent explanation. Thank you

[Ananya_Sharma]

How it became 6:00:10 and finishes at 6:00:15. and second time
Car Y starts at 6:00:10 and finishes at 6:00:20.
Could you please explain

[GMATGuruNY]

How it became 6:00:10 and finishes at 6:00:15. and second time
Car Y starts at 6:00:10 and finishes at 6:00:20.
Could you please explain

When a statement does not constrain the value of an unknown, one approach is to TEST different values for the unknown.
Statement 1 does not constrain Y's time.
For this reason, I tested two different values for Y's time.
In Case 1, I tested a time of 5 seconds for Y (from 6:00:10 to 6:00:15).
In Case 2, I tested a time of 10 seconds for Y (from 6:00:10 to 6:00:20).
In each case, X's time was 1 second less than Y's time.

The two cases helped illustrate the following:
While Y's actual time is unknown -- it could be 5 seconds, 10 seconds, or 1000 seconds -- statement 1 tells us the DIFFERENCE between X's time and Y's time:
Regardless of Y's time, X's time will always be ONE SECOND LESS than Y's time.

A more general proof:

Let Y's start time = 00:00:0A.
Let Y's end time = 00:00:0B.
Number of seconds for Y to cross the bridge = 00:00:0B - 00:00:0A = B-A.

Since X starts 3 seconds after Y, X's start time = 00:00:0[A+3}.
Since X finishes 2 seconds after Y, X's end time = 00:00:0[B+2}.
Number of seconds for X to cross the bridge = 00:00:0[B+2} - 00:00:0[A+3} = [B+2} - [A+3} = B-A-1.

Thus, X's time is 1 second less than Y's time.

[ngalinh]

Statement 1: Car X drove onto the bridge exactly 3 seconds after car Y drove onto the bridge and drove off the bridge exactly 2 seconds after car Y drove off the bridge.[/b]
Case 1:
Car Y starts at 6:00:10 and finishes at 6:00:15.
Total time = 5 seconds.
Car X starts at 6:00:13 (3 seconds after Car Y) and finishes at 6:00:17 (2 seconds after Car Y).
Total time = 4 seconds.

Case 2:
Car Y starts at 6:00:10 and finishes at 6:00:20.
Total time = 10 seconds.
Car X starts at 6:00:13 (3 seconds after Car Y) and finishes at 6:00:22 (2 seconds after Car Y).
Total time = 9 seconds.

The cases above illustrate that Car X's time is ONE SECOND LESS than Car Y's time.

Thanks Mitch! This is an excellent technique to conquer an abstract expression!

[Scott@TargetTestPrep]

If car X followed car Y across a certain bridge that is 1/2 mile long, how many seconds did it take car X to travel across the bridge?

(1) Car X drove onto the bridge exactly 3 seconds after car Y drove onto the bridge and drove off the bridge exactly 2 seconds after car Y drove off the bridge.
(2) Car Y traveled across the bridge at a constant speed of 30 miles per hour.

We are given that Car X follows Car Y across a bridge that is ½ mile long. We need to determine the time, in seconds, it took Car X to travel the ½ mile across the bridge.

Statement One Alone:

Car X drove onto the bridge exactly 3 seconds after Car Y drove onto the bridge and drove off the bridge exactly 2 seconds after Car Y drove off the bridge.

From statement one, we know that Car X gained 1 second on Car Y while the two cars traveled over the bridge. Thus, Car X took 1 second less than Car Y took to cross the bridge. However, without knowing the actual time it took Car Y to cross the bridge, we still don't know the number of seconds it took Car X to cross it. Statement one alone is insufficient to answer the question.

Statement Two Alone:

Car Y traveled across the bridge at a constant speed of 30 miles per hour.

From statement two we can determine the time it took Car Y to cross the bridge.

time = distance/rate

time = (1/2)/30

time = 1/60 hour

Since 1 hour = 3,600 seconds, 1/60 hour = 3,600 x 1/60 = 60 seconds.

We know that Car Y took 60 seconds to travel across the bridge. However, we do not know anything about Car X, so statement two is insufficient to answer the question.

Statements One and Two Together:

Because we know that that Car Y took 60 seconds to travel across the bridge and Car X took 1 second less, we know that it took Car X 59 seconds to travel across the bridge.

Answer: C