Answer:
[tex]t=1.5\ hours\ (running) \\ \\6-t=4.5\ hours\ (biking)\\ \\x=6\ miles \ ran\\ \\60-x=54\ miles \ biked[/tex]
Step-by-step explanation:
Ran:
Distance = x miles
Rate = 4 mph
Time = t hours
Then
[tex]x=4t[/tex]
Biked:
Distance = 60 - x miles
Rate = 12 mph
Time = 6 - t hours
Then
[tex]60-x=12(6-t)[/tex]
Substitute [tex]x=4t[/tex] into the second equation:
[tex]60-4t=12(6-t)\\ \\60-4t=72-12t\\ \\-4t+12t=72-60\\ \\8t=12\\ \\t=\dfrac{12}{8}=\dfrac{3}{2}=1.5\ hours\ (running) \\ \\6-t=6-1.5=4.5\ hours\ (biking)\\ \\x=4\cdot 1.5=6\ miles \ ran\\ \\60-6=54\ miles \ biked[/tex]
