If car X followed car Y across a certain bridge that is 21-m

Question

If car X followed car Y across a certain bridge that is 21-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.

Additional info on the problem 
Source: Paper Test
Test Code: 42
Section: 2 (Data Sufficiency)
Problem: 5

Bunuel · Answer

Let the time needed for car X to travel across the bridge be  t_x  seconds and the time for Y  t_y  seconds.

Question:  t_x=?

(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 --> car X needs 1 second less to travel across the bridge than car Y -->  t_y=t_x+1 . Not sufficient to calculate  t_x .

(2) Car Y traveled across the bridge at a constant speed of 30 miles per hour =  \frac{30}{3600}=\frac{1}{120}  miles per second --> car Y needs  t_y=\frac{21}{\frac{1}{120}}=21*120  seconds to travel across the bridge. Not sufficient to calculate  t_x .

(1)+(2)  t_y=t_x+1  and  t_y=21*120  -->  t_x=21*120-1 . Sufficient.

Answer: C.

niheil · Answer

Awesome! Thanks again, Bunuel. I wish you could take the GMAT for me, lol.

PennState08 · Answer

All,
This was a data sufficiency problem, but want to double check my math in case I see it in a problem solver.
If Car X followed Car Y across a certain bridge that is  \frac{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.
C is the correct answer for data sufficiency, but I want to go through the problem in various ways (problem solving) to make sure my math is correct.

Provided all the data; What are the rates of each Car? How many seconds would it take for Car X to catch Car Y? At what distance would Car X catch Car Y? 
 Rate Car X: ~30.5 mph OR  \frac{1}{118}  miles per second
Rate Car Y: 30 mph (given) OR  \frac{1}{120}  miles per second
Second for Car X to catch Car Y: 180 seconds OR 3 minutes OR  \frac{1}{20}  hour
Distance: 1.5 miles 
Explanations:
Rate x Time(t) = Distance
Car Y (given at 30 mph, so find  t  to solve for rate of car X)
 y  x  t  =  \frac{1}{2} 
30 x  t  =  \frac{1}{2}  (need miles per second, not hour)
 \frac{1}{120}  x  t  =  \frac{1}{2} 
 t  = 60 
Car X
 x  x ( t  - 1) =  \frac{1}{2}  ; 1 second for the time difference (waited 3 seconds after Y, finished 2 seconds after Y: 3 - 2 = 1)
 x  x (60 - 1) =  \frac{1}{2}  
 x  x 59 =  \frac{1}{2} 
 x  =  \frac{1}{118}

Time (in seconds) Car X catches Car Y:
 \frac{1}{118}  ( t  - 3) =  \frac{1}{120}t  ; 3 = amount of seconds after Y left.
 \frac{1}{118} t  -  \frac{3}{118}  =  \frac{1}{120}t 
 \frac{60}{7080}t  -  \frac{180}{7080}  =  \frac{59}{7080} 
 \frac{1}{7080} t  =  \frac{180}{7080} 
 t  = 180 seconds
180 seconds for Car X to catch Car Y

Distance (in miles) for Car X to catch Car Y
Taking either equation and substituting 180 for  t 
X)  \frac{1}{118}  x (180-3) = 1.5 miles
Y)  \frac{1}{120}  x (180) = 1.5 miles

I have all this set up correctly, right?

Bunuel · Answer

Merging similar topics. The only difference is in the length of the bridge (21 miles in first question and 1/2 miles in the second one). But the answer for both of them is C. Please ask if anything remains unclear.

Basshead · Answer

(1) This tells us Car X crosses the bridge 1 second faster than Car Y. We can't determine the time it took for Car X to cross the bridge.

(2) Car Y traveled across the bridge at a constant speed of 30 miles per hour. We can determine the time it takes Car Y to cross the bridge; however, this does not tell us anything about Car X

(1 & 2) From Statement 2 we can determine the time it takes Car Y to cross the bridge. We know Car X crosses the bridge 1 second faster than Car Y. Therefore, with both statements, we can determine the time it takes Car X to cross the bridge.

Hoozan · Answer

EducationAisle  based on (1) doesn't car X take 5 seconds longer that car Y? Why is this not correct?

EducationAisle · Answer

Not really 5 seconds Hoozan.

Car X 
a) drove onto the bridge exactly 3 seconds after car Y drove onto the bridge and 
b) drove off the bridge exactly 2 seconds after car Y drove off the bridge.

Notice that if X and Y had same speeds, then X would have driven off the bridge exactly 3 seconds after car Y drove off the bridge (because X drove onto the bridge exactly 3 seconds after car Y drove onto the bridge).

However, since X drove drove off the bridge exactly 2 seconds after car Y drove off the bridge, this would mean that X "caught up" with Y, 1 second, on the bridge. So, car X actually took 1 second less than car Y, to travel the bridge.

bumpbot · Answer

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If car X followed car Y across a certain bridge that is 21-m

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If car X followed car Y across a certain bridge that is 21-m

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