8.5 minutes per mile is equivalent to

17 minutes
----------------
2 miles

and the reciprocal of that is

2 miles
-----------
17 min

Now multiply 26.2 miles by

17 min (17 min)* (26.2 mi)
------------ , obtaining ---------------------------
2 miles 2 mi

This simplifies to (17)(26.2)/2 minutes = 222.7 minutes,

or

222.7 minutes 1 hr
-------------------- * ------------ = 3.7 hours
1 60 min

4 0

2 years ago

Find an equation of the line that passes through the points (-5, -3) and (3, 1)

Mkey [24]

$\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\quad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-5)}}}\implies \cfrac{1+3}{3+5}\implies \cfrac{4}{8}\implies \cfrac{1}{2}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{1}{2}}[x-\stackrel{x_1}{(-5)}]\implies y+3=\cfrac{1}{2}(x+5) \\\\\\ y+3=\cfrac{1}{2}x+\cfrac{5}{2}\implies y=\cfrac{1}{2}x+\cfrac{5}{2}-3\implies y = \cfrac{1}{2}x-\cfrac{1}{2}$