jennysussna wrote:
two cars are traveling on a highway in the same direction. if car A is traveling at a rate of 75 mph and is y miles ahead of car b, which is traveling at 60mpg, in terms of y, how many miles must car A travel to double the distance between itself and car b?
a 3y
b 4y
c 5y
d 6y
e 8y
This is an excellent opportunity to use "relative velocity" (in what we call the
chasing scenario), carefully explained in our method!
The "starting point" is shown in the figure attached.
Let B stay still (virtual velocity zero) and A travel at a virtual speed of 15mph (75-60).
The temporary focus is (always!) the virtual time (equal to the real one!), in this case, time for A to travel y (extra) miles in its virtual speed....
To find that, let´s use the powerful UNITS CONTROL!
\(y\,\,{\text{miles}}\,\,\left( {\frac{{1\,\,{\text{h}}}}{{15\,\,{\text{miles}}}}} \right)\,\,\, = \,\,\frac{y}{{15}}\,\,{\text{h}}\)
Finally we go back to A´s real velocity/speed, using again UNITS CONTROL:
\(?\,\, = \,\,\,75\,\,\left( {\frac{{{\text{miles}}}}{{\text{h}}}} \right)\,\, \cdot \,\,\frac{y}{{15}}\,\,{\text{h}}\,\,\,\,{\text{ = }}\,\,\,{\text{5y}}\,\,\,{\text{miles}}\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
fskilnik.
Attachments
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