Two cars are traveling side-by-side along the same road. At

Question

Cars.png Two cars are travelling side-by-side along the same road. At time 0, car 1 turns off onto another road. Two hours later, both cars are at the same horizontal position on their respective roads, as illustrated. If both cars were travelling at constant speeds for those entire two hours, how many times faster was car 1 travelling than car 2? (1) Car 1 travelled 80 miles during those two hours. (2) The two roads form a 60˚ angle.

Bunuel · Answer

Two cars are travelling side-by-side along the same road. At time 0, car 1 turns off onto another road. Two hours later, both cars are at the same horizontal position on their respective roads, as illustrated. If both cars were travelling at constant speeds for those entire two hours, how many times faster was car 1 travelling than car 2?

Look at the diagram below:

Attachment:

Roads.png [ 7.41 KiB | Viewed 5362 times ]

Car 1 covered the length of the hypotenuse and Car 2 traveled the length of the base. Since the cars traveled for equal time interval (2 hours), then the ratio of the speeds would be the same as the ratio of the distances, thus we are basically asked to find the value of hypotenuse/base.

(1) Car 1 traveled 80 miles during those two hours --> hypotenuse = 80, but we don't know the base. Not sufficient.

(2) The two roads form a 60˚ angle. We have a right triangle where the angles are 30°, 60°, and 90°. In such triangles the sides are always in the ratio \(1 : \sqrt{3}: 2\) (notice that the smallest side is opposite the smallest angle (30°), and the longest side is opposite the largest angle (90°)). Thus the ratio is 2:1. Sufficient.

Answer: B.

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fozzzy · Answer

If this question was worded a little different and we were asked to find the distance of car 2 then it would be C right?

Bunuel · Answer

Yes, that's correct.

pavan2185 · Answer

I missed exactly that point and chose C

. How to avoid such errors and to rephrase the questions clearly to understand what the question is asking?

WholeLottaLove · Answer

Two cars are travelling side-by-side along the same road. At time 0, car 1 turns off onto another road. Two hours later, both cars are at the same horizontal position on their respective roads, as illustrated. If both cars were travelling at constant speeds for those entire two hours, how many times faster was car 1 travelling than car 2?

Trying to solve this in two minutes, I misread the question and thought that the time spent traveling included distance before the car 1 and car 2 split up. I said the answer was E because we had no idea how for they drove on the straight line before car 1 departed the straight line. Obviously, this question is considering just how long they were driving starting from the point at which they hit the triangle.

(1) Car 1 travelled 80 miles during those two hours.
If the cars are aligned horizontally at the end of the trip then their coordinates form a triangle. The shallower the angle on the left side of the triangle, the less distance 1 is going to travel in relation to car 2. A steeper angle would mean that car 1 would travel more distance and would have to do it at a quicker speed if they were to converge at the same x-coordinate at the same time. We have no idea how many miles 2 traveled in this time. The angle could have been quite steep: car 2 could have traveled 4 miles and car 1 80 in which case car 1's speed is much greater than car 2's. The angle could have been very shallow and car 2 could have traveled 70 miles and car 1, 80, in which case their speeds would have been much closer. Insufficient.

(2) The two roads form a 60˚ angle. 
This tells us exactly what we need to know. Because both cars are aligned on the x-coordinate, they form a right angle. We know that the angle on the left of the triangle is 60 so this is a 30:60:90 triangle, the ratios of such are x: (√3/2 x): 2x meaning the ratio of the distance traveled by car 1 to car 2 is 2:1. Sufficient.

B.

mvictor · Answer

tricky question...
I selected C, but now I see why B is the answer.
we are asked not the real values, but the percentage of how fast the cars were, relatively to each other!

KrishnakumarKA1 · Answer

Prompt analysis
Two cars are travelling such that after the turn they land in same horizontal position

Superset
The value will be a positive real number greater than 1

Translation
In order to find the answer, we need:
1# exact speed of car 1 and car 2
2# the distance the cars have travelled in 2 hours
3# the relation in distances

Statement analysis
St 1: Speed of car 1 = 40mph. Cannot say anything about the car B. INSUFFICIENT
St 2: let the distance travelled by car 2 be x. Distance travelled by car 1 = x/cos60 = 2x . since the time taken by both the cars is same, therefore ratio of speed will be equal to ratio of distance.
Speed of car 1/speed of car 2 = 2x/x = 2. ANSWER

Option B

bumpbot · Answer

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Two cars are traveling side-by-side along the same road. At

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