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# The driver of a car traveling at a speed of 40 miles per hour had to

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The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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29 Nov 2018, 01:14
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Difficulty:

55% (hard)

Question Stats:

57% (02:41) correct 43% (02:29) wrong based on 51 sessions

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The driver of a car traveling at a speed of 40 miles per hour had to stop the car quickly. If the drivers reaction time was 3/4 of a second, approximately how many feet did the car travel during the drivers reaction time? (1 mile = 5,280 feet)

A. 30
B. 45
C. 60
D. 75
E. 90

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Re: The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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30 Nov 2018, 09:40
Bunuel
This is the approach which i followed

Speed = 40 miles per hour = $$\frac{40}{60*60}$$*5280 feet per second
= $$\frac{176}{3}$$

the drivers reaction time was 34 of a second = $$\frac{1}{34}$$

Therefore distance = $$\frac{176}{3}$$ * $$\frac{1}{34}$$

But there is no option close to what i found as solution.

can you please tell what is meant by 34 of a second and is it right what i have taken ?

what is the right approach?
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Re: The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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30 Nov 2018, 11:36
Bunuel wrote:
The driver of a car traveling at a speed of 40 miles per hour had to stop the car quickly. If the drivers reaction time was 34 of a second, approximately how many feet did the car travel during the drivers reaction time? (1 mile = 5,280 feet)

A. 30
B. 45
C. 60
D. 75
E. 90

speed would be 40*5280/(60*60)= 58.66 feet per sec

reaction time is 1/34 of a second= 34/60 = 0.56 sec

so distance in feet the car would travel : 58.66*0.56= ~34 but answer choice is not given..

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Re: The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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30 Nov 2018, 16:36
After testing out the calculations, I am pretty sure that the question is supposed to say, "If the driver's reaction time was $$\frac{3}{4}$$ of a second..." If we use $$\frac{3}{4}$$ of a second as the reaction time, the calculation of the distance becomes:

$$40 \frac{miles}{hour} * \frac{3}{4} seconds * \frac{1 hour}{3600 seconds} * \frac{5280 feet}{1 mile}$$

The units work out to feet, so if we just write out the numerical calculations they look like:

$$40 * \frac{3*5280}{4*3600}$$

If we take factors of 3 and 4 out of both the numerator and denominator, we get:

$$40 * \frac{1320}{1200}$$

At this point, we might recognize that 1320/1200 = 1.1, or at least see that it's just a little larger than 1. Looking at the answer choices, the only one that's a little larger than 40 is B, 45. (There is no way that 1320/1200 is close to 1.5, which is what it would have to be to give us answer choice C.)

Please let me know if you have any questions!
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Re: The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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01 Dec 2018, 03:37
JeffYin wrote:
After testing out the calculations, I am pretty sure that the question is supposed to say, "If the driver's reaction time was $$\frac{3}{4}$$ of a second..." If we use $$\frac{3}{4}$$ of a second as the reaction time, the calculation of the distance becomes:

$$40 \frac{miles}{hour} * \frac{3}{4} seconds * \frac{1 hour}{3600 seconds} * \frac{5280 feet}{1 mile}$$

The units work out to feet, so if we just write out the numerical calculations they look like:

$$40 * \frac{3*5280}{4*3600}$$

If we take factors of 3 and 4 out of both the numerator and denominator, we get:

$$40 * \frac{1320}{1200}$$

At this point, we might recognize that 1320/1200 = 1.1, or at least see that it's just a little larger than 1. Looking at the answer choices, the only one that's a little larger than 40 is B, 45. (There is no way that 1320/1200 is close to 1.5, which is what it would have to be to give us answer choice C.)

Please let me know if you have any questions!

JeffYin this question is printed wrong ?
What do you think of my approach ? was i going in right direction ?
is it suppose to solve in that way only ?
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Re: The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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01 Dec 2018, 10:49
1
soapbolt wrote:
Bunuel
This is the approach which i followed

Speed = 40 miles per hour = $$\frac{40}{60*60}$$*5280 feet per second
= $$\frac{176}{3}$$

the drivers reaction time was 34 of a second = $$\frac{1}{34}$$

Therefore distance = $$\frac{176}{3}$$ * $$\frac{1}{34}$$

But there is no option close to what i found as solution.

can you please tell what is meant by 34 of a second and is it right what i have taken ?

what is the right approach?

Hi soapbolt,

I think your approach was good, and you would have gotten the right answer if the question clearly stated that the reaction time is $$\frac{3}{4}$$ second rather than $$\frac{1}{34}$$ second.

Strategy-wise, in order to be more efficient, I suggest not reducing the fraction until the last step in your calculation, because you might see that you don't need to do all of the calculations to get the right answer. For example, the way you wrote your initial calculation, if you multiplied that by $$\frac{3}{4}$$, you would have ended up with the fraction:

$$\frac{40*5280*3}{60*60*4}$$

At this point, you might recognize that $$\frac{40*3}{60*4} = \frac{1}{2}$$, which would leave you with just

$$\frac{5280}{60*2} = \frac{5280}{120}$$

Looking at the answer choices, it should be clear that this is closest to 45, and you might have avoided doing some calculations.

Still, your approach was correct, and you probably would have gotten the answer in a relatively short amount of time, so there's nothing wrong with what you did!
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Re: The driver of a car traveling at a speed of 40 miles per hour had to  [#permalink]

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06 Dec 2018, 03:01
JeffYin wrote:
After testing out the calculations, I am pretty sure that the question is supposed to say, "If the driver's reaction time was $$\frac{3}{4}$$ of a second..." If we use $$\frac{3}{4}$$ of a second as the reaction time, the calculation of the distance becomes:

$$40 \frac{miles}{hour} * \frac{3}{4} seconds * \frac{1 hour}{3600 seconds} * \frac{5280 feet}{1 mile}$$

The units work out to feet, so if we just write out the numerical calculations they look like:

$$40 * \frac{3*5280}{4*3600}$$

If we take factors of 3 and 4 out of both the numerator and denominator, we get:

$$40 * \frac{1320}{1200}$$

At this point, we might recognize that 1320/1200 = 1.1, or at least see that it's just a little larger than 1. Looking at the answer choices, the only one that's a little larger than 40 is B, 45. (There is no way that 1320/1200 is close to 1.5, which is what it would have to be to give us answer choice C.)

Please let me know if you have any questions!

distance = (40 x 5280)/(60 x 60) * (3/4)=(4 x 528)/(6 x 6) * (3/4) = 528/(2 x 6) = 264/6 = 44
the nearest is 45
Re: The driver of a car traveling at a speed of 40 miles per hour had to   [#permalink] 06 Dec 2018, 03:01
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