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.
If Albert can travel 200 miles in 4 hours, how many hours
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It will take Albert (350/200)*4 = 7 hrsBTGmoderatorLU 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.
The correct answer: C
Hope this helps!
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Since Albert has a rate of 200/4 = 50 mph, it will take him 350/50 = 7 hours to travel 350 miles.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
Answer: C
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\[200\,\,{\text{miles}}\,\,\,\, \leftrightarrow \,\,\,\,{\text{4}}\,\,{\text{h}}\]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
\[{\text{350}}\,\,\,{\text{miles}}\,\,\, \leftrightarrow \,\,\,{\text{?}}\,\,{\text{h}}\]
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?
This solution follows the notations and rationale taught in the GMATH method.
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And now a solution that our advanced students do as "second nature":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
\[350\,{\text{miles}}\,\,\,\left( {\frac{{4\,\,{\text{h}}}}{{200\,\,{\text{miles}}}}\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}\,\,} \right)\,\,\, = \frac{{35 \cdot 4}}{{20}} = 7\,\,\,\,\left[ {\text{h}} \right]\]
Obs.: arrows indicate licit converter.
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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And let´s offer a third possibility.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
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.
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Since Albert travels 200 miles in 4 hours, his rate = 200/4 = 50 mph.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
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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Another approach is to apply some number senseBTGmoderatorLU 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.
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