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?
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
