Respuesta :
Answer:
The speed does he run is 3 miles/hr and her cycling speed is 18 miles/hr.
Step-by-step explanation:
Consider the provided information.
Let x mi/h represents the rate of running and y mi/h represents the rate of cycling.
Monday she spends 1/3 hour at each activity, covering a total of 7 miles.
[tex]\frac{1}{3}x+ \frac{1}{3}y=7[/tex]
[tex]x+y=21[/tex]
[tex]x=21-y[/tex]
On Tuesday, she runs for 17 minutes and cycles for 40 minutes, covering a total of 12.85 miles.
Convert minutes to hours by dividing 60.
[tex]\frac{17}{60}x+ \frac{40}{60}y=12.85[/tex]
[tex]17x+40y=771[/tex]
Substitute x = 21-y in above equation,
[tex]17(21-y)+40y=771[/tex]
[tex]357-17y+40y=771[/tex]
[tex]23y=771-357[/tex]
[tex]23y=414[/tex]
[tex]y=18[/tex]
Substitute the value of y in [tex]x=21-y[/tex]
[tex]x=21-18[/tex]
[tex]x=3[/tex]
Hence, the speed does he run is 3 miles/hr and her cycling speed is 18 miles/hr.
