**Quote:**

A car travels through a path 1 mile long at a speed of r miles per hour. If it travels at a speed of r+20 miles per hour, it would cover the path in 4 minutes less. What is the value of r?

A) 30

B) 20

C) 10

D) 8

E) 5

Units control is one of the most powerful tools of the GMATH method:

\(\frac{{1\,\,mile}}{{r\,\,mph}}\,\, = \,\,\frac{1}{r}\,\,h\,\,\,\left( {\frac{{60\min }}{{1h}}} \right)\,\,\,\, = \,\,\,\frac{{60}}{r}\,\,\,\min \,\,\,\,\,\,\,\left( {{\text{original}}\,\,{\text{time}}} \right)\)

\(\frac{{1\,\,mile}}{{\left( {r + 20} \right)\,\,mph}}\,\, = \,\,\frac{1}{{r + 20}}\,\,h\,\,\,\left( {\frac{{60\min }}{{1h}}} \right)\,\,\,\, = \,\,\,\frac{{60}}{{r + 20}}\,\,\,\min \,\,\,\,\,\,\,\left( {{\text{less}}\,\,{\text{time}}} \right)\)

\(\frac{{60}}{r} - \frac{{60}}{{r + 20}} = 4\)

Now simply PLUG-IN the alternative choices.

The solution above follows the notations and rationale taught in the GMATH method.

_________________

Fabio Skilnik :: http://www.GMATH.net (Math for the GMAT)

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