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# An automotive test consisted of driving a car the same distance three

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Math Expert
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An automotive test consisted of driving a car the same distance three  [#permalink]

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12 Feb 2015, 07:13
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Difficulty:

75% (hard)

Question Stats:

60% (02:29) correct 40% (02:25) wrong based on 193 sessions

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An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 37 hours to complete, how many miles was the car driven during the entire test?

A. 400
B. 600
C. 1200
D. 1800
E. 2400

Kudos for a correct solution.

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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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Updated on: 12 Feb 2015, 09:18
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1
time= distance /speed

lets say distance is d
$$\frac{d}{40}+ \frac{d}{50}+ \frac{d}{60}$$ = 37 hours

which gives d= 600

so total distance is 1800

Originally posted by ynaikavde on 12 Feb 2015, 07:22.
Last edited by ynaikavde on 12 Feb 2015, 09:18, edited 1 time in total.
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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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22 Feb 2015, 23:04
1
Hi All,

This question (and its answers) are full of Number Property rules and patterns that you can take advantage of. It can easily be solved by TESTing THE ANSWERS.

We're told that a driving test drove the SAME distance at 3 different speeds: 40mph, 50mph and 60mph. We're also told that the TOTAL time for these 3 tests was 37 hours. We're asked for the TOTAL distance traveled.

To start, 37 hours EXACTLY is an interesting number. Given the speeds that we have to work with (and the total of 37 hours), we're probably NOT going to be dealing with fractions, so it's likely that we're looking for a distance that is a MULTIPLE of 40, 50 and 60. Also, IF we had driven the entire 37 hours at 40 mph (which we know that we didn't), we'd have gone OVER 1200 miles. Since some of that time was spent going 50mph and 60mph, the distance is clearly much GREATER than 1200 miles.

This leaves us with just 2 possible answer choices: D and E.

IF....
Total distance = 1800 miles, then each "leg" of the trip = 600 miles.

600 miles at 40mph = 15 hours
600 miles at 50mph = 12 hours
600 miles at 60mph = 10 hours
Total time = 15+12+10 = 37 hours.
This is a MATCH for what we were told.

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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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12 Feb 2015, 08:51
ans D 1800..
let x be the distance..
so time taken by three cars is x/40,x/50,x/60... total time taken= x/40+x/50+x/60=x*37/600 =37(given)
x=600... total =3x=1800...
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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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16 Feb 2015, 06:26
Bunuel wrote:
An automotive test consisted of driving a car the same distance three separate times, first at an average rate of 40 miles per hour, then 50 miles per hour, then 60 miles per hour. If the test took 37 hours to complete, how many miles was the car driven during the entire test?

A. 400
B. 600
C. 1200
D. 1800
E. 2400

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Explanation: Solution: D If the distance for each drive is d, then the time for each drive is d divided by the rate for that drive. The sum of all the times is given: 37 hours. Therefore, d/40 + d/50 + d/60 = 37.

With a common denominator of 600, we can write this as 15d/600 + 12d/600 + 10d/600 = 37, and therefore 37d/600 = 37. This means that d = 600. All together the car was driven 3 times, so it was driven 1800 miles.
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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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24 Feb 2015, 21:35

Let the total distance covered = d

Its divided into 3 equal segments of d/3

Setting up the time equation

$$\frac{d}{40*3} + \frac{d}{50*3} + \frac{d}{60*3} = 37$$

d = 1800
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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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26 Jan 2017, 22:39
The question is fairly a simple one. However, I see a trap answer of B. This is trapping those who fall into a classic mistake pattern - READ THE QUESTION and then KEEPING TRACK.

The question asks for a total distance that is driven and not the distance for each trip , which is a constant. If we are solving for
37 = d/40+d/50+d/60, then we get d = 600. Forgetting to track what the question asked will lead us to B. The question asks for 3*d = 1800.

I have made that same error. I understand that if we were not making timing decisions along the test wisely, we may be tempted to make an error. The test is taking advantage right there!
Be careful guys
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Re: An automotive test consisted of driving a car the same distance three  [#permalink]

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26 Nov 2019, 08:42
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Re: An automotive test consisted of driving a car the same distance three   [#permalink] 26 Nov 2019, 08:42
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