Question

A girl runs at 5 miles per hour and bikes at 10 miles per hour. In a week she bikes and runs a total of 200 miles. She bikes twice as much as she runs. How many hours did she spend biking?

Answer 1

Answer: $16\ hours$.

Step-by-step explanation:

Let be "r" the number of hour the girl spent running and "b" the number of hour the girl spent biking.

Set up a system of equations:

$\left \{ {{5r+10b=200} \atop {b=2r}} \right.$

Applying the Substitutition method, you can substitute the second equation into the first one and solve for "r". Then:

$5r+10(2r)=200\\\\25r=200\\\\r=\frac{200}{25}\\\\r=8$

Finally, you must substitute the value of "r" into the second equation in order to find "b". So, this is:

$b=2(8)\\\\b=16$