Question 1207782
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1. Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. During <s>Explaining Concepts:Discussion and Writing</s> your run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?
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In case helpful, you can arrange the information described in a table.

{{{SPEED*TIME=DISTANCE}}}

<pre>
             SPEEDS         TIME            DISTANCE

RUN             6

BIKE           25

Total                        5                   87
</pre>
And you can figure what to do now from this. 



<pre>
             SPEEDS         TIME            DISTANCE

RUN             6           5-x              6(5-x)

BIKE           25            x               25x

Total                        5                 87
</pre>
{{{highlight_green(6(5-x)+25x=87)}}}


{{{25x-6x+30=87}}}

{{{19x=87-30}}}

{{{x=(87-30)/19}}}

{{{highlight_green(x=3)}}}


Simple arithmetic from there.
Distance running, {{{12}}} miles.
Distance biking, {{{75}}} miles.