Question

A woman keeps fit by bicycling and running every day. Monday she spends hour at each activity, covering a total of 7 miles. On Tuesday, she runs for 17 minutes and cycles for 40 minutes, covering a total of 12.85 miles. Assuming her running and cycling speeds don't change from day to day, at what speed does she run and cycle?

Answer 1

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.

$\frac{1}{3}x+ \frac{1}{3}y=7$

$x+y=21$

$x=21-y$

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.

$\frac{17}{60}x+ \frac{40}{60}y=12.85$

$17x+40y=771$

Substitute x = 21-y in above equation,

$17(21-y)+40y=771$

$357-17y+40y=771$

$23y=771-357$

$23y=414$

$y=18$

Substitute the value of y in $x=21-y$

$x=21-18$

$x=3$

Hence, the speed does he run is 3 miles/hr and her cycling speed is 18 miles/hr.