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Sub 505 (Easy)|   Distance and Speed Problems|                     
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Bunuel
SOLUTION

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?

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

(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. 30 miles per hour is \(\frac{30}{3600}=\frac{1}{120}\) miles per second --> car Y needs \(t_y=\frac{(\frac{1}{2})}{(\frac{1}{120})}=60\) seconds to travel across the bridge. Not sufficient to calculate \(t_x\).

(1)+(2) \(t_y=t_x+1\) and \(t_y=60\) --> \(t_x=60-1=59\). Sufficient.

Answer: C.
­I keep having trouble visualizing this type of question.

(Statement 1):
- Car X drove onto the bridge exactly 3 seconds after Car Y -> so does this mean car X is at the beginning of the bridge and car Y already travels a distance worth of 3 seconds?
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hughng92

Bunuel
SOLUTION

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?

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

(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. 30 miles per hour is \(\frac{30}{3600}=\frac{1}{120}\) miles per second --> car Y needs \(t_y=\frac{(\frac{1}{2})}{(\frac{1}{120})}=60\) seconds to travel across the bridge. Not sufficient to calculate \(t_x\).

(1)+(2) \(t_y=t_x+1\) and \(t_y=60\) --> \(t_x=60-1=59\). Sufficient.

Answer: C.
­I keep having trouble visualizing this type of question.

(Statement 1):
- Car X drove onto the bridge exactly 3 seconds after Car Y -> so does this mean car X is at the beginning of the bridge and car Y already travels a distance worth of 3 seconds?

Yes, that's correct. Imagine Car Y entered the bridge at 00:00:00, and then Car X entered it exactly 3 seconds later, at 00:00:03. By that time, Car Y had already been moving on the bridge for 3 seconds.
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