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If Albert can travel 200 miles in 4 hours, how many hours

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If Albert can travel 200 miles in 4 hours, how many hours

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Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10

The OA is C.

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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10

The OA is C.
It will take Albert (350/200)*4 = 7 hrs

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10
Since Albert has a rate of 200/4 = 50 mph, it will take him 350/50 = 7 hours to travel 350 miles.

Answer: C

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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, travelling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10
\[200\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{4}}\,\,{\text{h}}\]
\[{\text{350}}\,\,\,{\text{miles}}\,\,\, \leftrightarrow \,\,\,{\text{?}}\,\,{\text{h}}\]
Same constant rate (speed) implies that the ratio miles/time is constant (and different from zero): we have direct proportionality.
\[\frac{{\text{?}}}{4} = \frac{{350}}{{200}}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\frac{{{\text{?}} \cdot \boxed{50}}}{{4 \cdot \boxed{50}}} = \frac{{350}}{{200}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{350}}{{50}} = 7\,\,\,\left[ {\text{h}} \right]\,\,\]
(*) This is what we call the "Bruce Lee" technique, because he is known to have said: "Punch when you have to punch. Kick when you have to kick." ... and he certainly thought about "denominator equal to the denominator, imply numerator equal to the numerator"... got it? Wink

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

Regards,
Fabio.

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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10
And now a solution that our advanced students do as "second nature":
\[350\,{\text{miles}}\,\,\,\left( {\frac{{4\,\,{\text{h}}}}{{200\,\,{\text{miles}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}\,\,} \right)\,\,\, = \frac{{35 \cdot 4}}{{20}} = 7\,\,\,\,\left[ {\text{h}} \right]\]
Obs.: arrows indicate licit converter.

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

Regards,
Fabio.

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Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10
And let´s offer a third possibility.

This one is dedicated to Julia, my 10-years old niece:
\[200\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{4}}\,\,{\text{h}}\]
\[{\text{50}}\,\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{1}}\,\,{\text{h}}\]
\[{\text{350}}\,\,\,{\text{miles}}\,\,\, \leftrightarrow \,\,\,{\text{?}}\,{\text{ = }}\,{\text{7}}\,\,\,{\text{h}}\]

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?

A. 5
B. 6
C. 7
D. 8
E. 10
Since Albert travels 200 miles in 4 hours, his rate = 200/4 = 50 mph.
When the correct answer is divided into 350 miles, the resulting rate must be 50 mph.
Only C works:
350/7 = 50.

The correct answer is C.

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BTGmoderatorLU wrote:
Source: Princeton Review

If Albert can travel 200 miles in 4 hours, how many hours will it take Albert, traveling at the same constant rate, to travel 350 miles?
A. 5
B. 6
C. 7
D. 8
E. 10
The OA is C.
Another approach is to apply some number sense

GIVEN: Albert can travel 200 miles in 4 hours
This means: Albert can travel 100 miles in 2 hours [if we reduce the travel time by 50%, we reduce the distance traveled by 50%]
And: Albert can travel 50 miles in 1 hour [if we reduce the travel time by 50%, we reduce the distance traveled by 50%]

350 miles = 200 miles + 100 miles + 50 miles
So, the time to travel 350 miles = 4 hours + 2 hours + 1 hours = 7 HOURS

Answer: C

Cheers,
Brent

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