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The rear wheels of a car crossed a certain line 0.5 second

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The rear wheels of a car crossed a certain line 0.5 second

by AAPL » Wed Oct 17, 2018 11:38 am

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The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)

$$A.\ \left(\frac{20}{5280}\right)\left(\frac{60^2}{0.5}\right)$$
$$B.\ \left(\frac{20}{5280}\right)\left(\frac{60}{0.5}\right)$$
$$C.\ \left(\frac{20}{5280}\right)\left(\frac{0.5}{60^2}\right)$$
$$D.\ \frac{\left(20\right)\left(5280\right)}{\left(60^2\right)\left(0.5\right)}$$
$$E.\ \frac{\left(20\right)\left(5280\right)}{\left(60\right)\left(0.5\right)}$$
OA A
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by Jay@ManhattanReview » Wed Oct 17, 2018 11:39 pm
AAPL wrote:GMAT Prep

The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)

$$A.\ \left(\frac{20}{5280}\right)\left(\frac{60^2}{0.5}\right)$$
$$B.\ \left(\frac{20}{5280}\right)\left(\frac{60}{0.5}\right)$$
$$C.\ \left(\frac{20}{5280}\right)\left(\frac{0.5}{60^2}\right)$$
$$D.\ \frac{\left(20\right)\left(5280\right)}{\left(60^2\right)\left(0.5\right)}$$
$$E.\ \frac{\left(20\right)\left(5280\right)}{\left(60\right)\left(0.5\right)}$$
OA A
Given The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart,

Speed of the car = Distance / time = 20/0.5 feet/second = (20/5280)/0.5 mile/second = 20/(0.5*5280) mile/second = (20*3600)/(0.5*5280) mile/hour = [20/5280] * [(60^2)/0.5] mile/hour

The correct answer: A

Hope this helps!

-Jay
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by fskilnik@GMATH » Thu Oct 18, 2018 4:50 am
AAPL wrote:GMAT Prep

The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)

$$A.\ \left(\frac{20}{5280}\right)\left(\frac{60^2}{0.5}\right) \,\,\,\,\,\, B.\ \left(\frac{20}{5280}\right)\left(\frac{60}{0.5}\right) \,\,\,\,\,\, C.\ \left(\frac{20}{5280}\right)\left(\frac{0.5}{60^2}\right) \,\,\,\,\,\, D.\ \frac{\left(20\right)\left(5280\right)}{\left(60^2\right)\left(0.5\right)} \,\,\,\,\,\, E.\ \frac{\left(20\right)\left(5280\right)}{\left(60\right)\left(0.5\right)}$$
$$1\,\,{\rm{mile}}\,\,\, \leftrightarrow \,\,\,5280\,\,{\rm{feet}}$$
$$V\left( {{\rm{speed}}} \right) = {{\,20\,\,{\rm{feet }}} \over {0.5\,\,{\rm{s}}}}\,\, = \,\,\,?\,\,{\rm{mph}}$$
Perfect opportunity to use UNITS CONTROL, one of the most powerful tools of our course!
$$?\,\,\, = \,\,\,{{\,20\,\,{\rm{feet }}} \over {0.5\,\,{\rm{s}}}}\left( {{{1\,\,{\rm{mile}}} \over {5280\,\,{\rm{feet}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\left( {{{60\,\,{\rm{s}}} \over {1\,\,{\rm{min}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\left( {{{60\,\,{\rm{min}}} \over {1\,\,{\rm{h}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right)\,\,\, = \,\,\,{{20 \cdot 60 \cdot 60} \over {0.5\,\, \cdot 5280}}\,\,\,\,\left[ {{\rm{mph}}} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( A \right)$$
Obs.: arrows indicate licit converters.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Thu Oct 18, 2018 5:29 pm
AAPL wrote:GMAT Prep

The rear wheels of a car crossed a certain line 0.5 second after the front wheels crossed the same line. If the centers of the front and rear wheels are 20 feet apart and the car traveled in a straight line at a constant speed, which of the following gives the speed of the car in miles per hour? (5280 feet = 1 mile)

$$A.\ \left(\frac{20}{5280}\right)\left(\frac{60^2}{0.5}\right)$$
$$B.\ \left(\frac{20}{5280}\right)\left(\frac{60}{0.5}\right)$$
$$C.\ \left(\frac{20}{5280}\right)\left(\frac{0.5}{60^2}\right)$$
$$D.\ \frac{\left(20\right)\left(5280\right)}{\left(60^2\right)\left(0.5\right)}$$
$$E.\ \frac{\left(20\right)\left(5280\right)}{\left(60\right)\left(0.5\right)}$$
OA A
We see that the car traveled 20 ft in 0.5 seconds. Since the car traveled at a constant speed, its rate was 20 ft/0.5 seconds.

Let's convert 20 ft/0.5 sec into mph:

20 ft/0.5 sec x 1 mi/5280 ft x 3600 sec/1 hr

In the above expression, we see the units "seconds" and "feet" will cancel and we are left with:

(20 x 1 x 3600)/(0.5 x 5280 x 1) mi/hr

(20 x 3600)/(0.5 x 5280) mi/hr

(20 x 60^2) / (0.5 x 5280) mi/hr

Answer: A

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by [email protected] » Thu Oct 18, 2018 6:28 pm
Hi All,

Since this question is wordy and the answers are somewhat "crazy"-looking, it's possible that you might feel overwhelmed by this prompt. If you stay calm though and do the unit conversions properly, then you can use the answer choices to your advantage (and eliminate most of them for being too big or too small). Here's how:

The first step is to figure out approximately how fast the car was going. This will take a little bit of work, but the individual steps are not too hard. The information in the first part of the question tells us that it basically takes .5 seconds to travel 20 feet. Since the question asks for a speed in MILES per HOUR, we have to convert these numbers....

.5 seconds = 20 feet
1 second = 40 feet
60 seconds = 2400 feet
1 hour = (2400)(60) = 144,000 feet

Since 5280 feet = 1 mile....
144,000 feet = about 28 miles

So the car was traveling about 28 miles per hour.

Now, by paying attention to how the answer choices are "structured", we can eliminate the wrong answers without having to calculate much...Remember that we're looking for an answer that is approximately 28.....

Let's start with Answers B and C, since they're the easiest to eliminate. Look at the NUMERATORS (relative to the DENOMINATORS)....

Answer B: 1200/2640. This is a FRACTION less than 1. Eliminate B.

Answer C: 10/(GIGANTIC PRODUCT). This is a REALLY small fraction. Eliminate C.

Of the remaining 3 answers, Answer E is reasonably easy to eliminate....

Answer E: (20)(5280)/30 This will be in the THOUSANDS. It's much too BIG. Eliminate E.

Between Answers A and D, notice how the "20" and the "0.5" are in the same relative positions.....

20/.05 = 40

So we're multiplying some fraction by 40. To get an answer that is equal to about 28, we need that fraction to be LESS than 1...

Answer A: 60^2/5280 is LESS than 1

Answer D: 5280/60^2 is GREATER than 1. Eliminate D.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
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