swerve wrote:Kevin drove from A to B at a constant speed of 60 mph. Once he reached B, he turned right around without pause, and returned to A at a constant speed of 80 mph. Exactly 4 hours before the end of his trip, he was still approaching B, only 15 miles away from it. What is the distance between A and B?
A. 275 miles
B. 300 miles
C. 320 miles
D. 350 miles
E. 390 miles
Source: Magoosh
\[? = d\,\,\,\left[ {{\text{miles}}} \right]\]
Excellent opportunity to use UNITS CONTROL, one of the most powerful tools of our course!
\[\left[ {\text{h}} \right] = \frac{{\left[ {{\text{miles}}} \right]}}{{\left[ {{\text{mph}}} \right]}}\]
From "Exactly 4 hours before the end of his trip, he was still approaching B, only 15 miles away from it. " we have:
\[4 = {T_{{\text{CB}}}} + {T_{{\text{BC}}}} + {T_{{\text{CA}}}} = \frac{{15}}{{60}} + \frac{{15}}{{80}} + \frac{{d - 15}}{{80}} = \frac{{1 \cdot \boxed{20}}}{{4 \cdot \boxed{20}}} + \frac{d}{{4 \cdot 20}} = \frac{{d + 20}}{{80}}\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ {\text{h}} \right]\]
\[\frac{{d + 20}}{{80}} = 4\,\,\,\, \Rightarrow \,\,\,\,\,? = d = 4 \cdot 80 - 20 = 300\,\,\,\,\,\left[ {{\text{miles}}} \right]\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
