A car moving at an average speed of x miles/hr, traveled

A car moving at an average speed of x miles/hr, traveled for x minutes. Did the car travel more than 100 miles?

Note that with this problem the car travels the same number of miles as it spends minutes on the road.

1. The car traveled the second half of the distance in the same time it took to travel the first half.
All this tells us is that the car spent the same amount of time covering the 2nd half of the journey as it did the first. It could have traveled 20 miles/hr for 20 minutes or 100 miles/hr in 100 minutes.
INSUFFICIENT

2. The car traveled the first half in 30 minutes at the speed of x miles/hr.
The stem tells us that the car moves at an average of x miles/hr and traveled for x minutes. In this case, we are told that the car traveled the first 30 minutes at speed x, so according to the stem it traveled the first half in 30 minutes at 30 miles/hour. If it covered 1/2 of the journey in 30 minutes at 30 miles/hour it traveled 15 miles. If 1/2 of the journey was 15 miles then the 2nd half must be 15 miles as well. It did not cover more than 100 miles.
SUFFICIENT

(B)

Although I got the question right it appears that some of my math was incorrect. For #2 it tells us that it travels the first half in 30 minutes at the speed of x miles/hr. In other words (the way I read it according to the stem) the car traveled 30 MPH which means that in one hour it traveled 30 miles, not 60. What am I doing wrong here?

Thanks!

you have missed this- A car moving at an average speed of x miles/hr, traveled for x minutes

means total time is the avgspeed of entire journey not the time of first half that is 30 min
X= 30min(first half)+ 30min(second half)= 60 min That leads to 60 mile/hour..
I hope it is clear now.

Thanks for the response.

I see your logic but I think I am confused by the wording of the problem.

Here is my (incorrect) reasoning: Car x travels 30 minutes at x miles/hour. According to the stem, a car travels at x miles/hour for x minutes. In other words, the time the car spends on the road is how many miles/hour it travels. It travels the first half in 30 minutes at a rate of 30 miles/hour. In other words over the course of 30 minutes it travels 15 miles.

I believe the correct methodology is: If the car travels the first half in 30 minutes then it takes an hour to complete the trip (i.e. 60 minutes) so according to the stem it does 60 miles/hour in 60 minutes or 60 miles. I just don't understand why it's solved this way as opposed to the way I did it.

Hi,

The x minutes given in the stem is the total time taken. For example if the car travels for 30 minutes in the first half it totally takes 60 minutes . Therefore the speed is 60 miles /hour

Solution

Speed is given as x miles/hr and time traveled is given as x minutes or x/60 hrs. We need to find the total distance traveled i.e., x*x/60. In other words if we can find x we can answer the question.

Statement 1:Time traveled is the same in both the halves. So the speed is also the same. Taking the stem into account we know the time taken is x/2 minutes in each half and the speed is x miles /hr in each half and the distance traveled is (x*x / 60)/2 in each half. But we cannot find x based on the above information. So this statement by itself is insufficient.

Statement 2: The car traveled 30 minutes in the first half. It traveled at the speed of x miles/hour. Since the average speed of the travel is x miles/hr too, the car should have traveled at the same speed in the second half also and therefore traveled for the same time it traveled in the first half. The total time taken is 30+ 30 minutes= 60 minutes. We have found out x as 60. Speed is therefore 60 miles /hr. Total distance is x*x/60 = 60 miles. Now we can answer the question because we know x. Thus this statement by itself is sufficient.

Therefore answer B.

I see now. The stem is referring to the entire trip, not just one part of 1/2 of it. I am not used to the wording of these questions so I think more review will help me. I admit though, I am still a bit confused as to how #2 can say 30 minutes and why we don't plug in 30 for x for 30 miles/hour.

Thanks for the response!

time taken = \(x/60\) hr, speed = \(x\) miles/hr
distance = \(x^2/60\)

question is \(x^2/60\) > 100 ? => \(x^2 > 6000\) ?

Statement 1: time taken for the first half is same as time taken for the second half
half-distance = \(x^2/120\)
\(x^2/(120 * v1) = x^2/(120 * v2)\) => \(v1 = v2\)
no info about x, as x cancels each other => insuff

Statement 2: The car traveled the first half in 30 minutes at the speed of x miles/hr.
time taken for half distance = \(x^2/(120 * x)\) = 1/2 (30 mins)
=> \(x = 60\) => \(x^2 < 6000\) => answers our question as NO

Answer (B)

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