Question

As part of Kayla's exercise program, she either runs 6 miles/day or rides her bike 10 miles/day. Her new goal is to cover a minimum distance of 200 miles, with at least 15 of the days running. She would like to determine the number of days it would take to accomplish this.

Answer 1

Kayla will be able to cover the distance of 200 miles by riding bike for 11 days and by running for 15 days.

Explanation:

Numbers of days Kayla's has to run be x

Numbers of days Kayla's has to ride bike be y

Speed while running = 6 miles/day

Distance covered by running in x days = 6miles/day × x

Speed while riding a bike = 10 mile/day

Distance covered by riding bike in y days = 10 miles/day × y

Distance desired by Kayla to cover = 200 miles

`200miles=6 miles/day* x+10 miles/day * y`

At least 15 of the days running.Put x = 15 days in above equation:

`200miles=6 miles/day* 15 days+10 miles/day * y`

`200 miles - 90 miles=10 miles/day * y`

`(110 miles)/(10 miles/day)=y`

y= 11 days

Kayla will be able to cover the distance of 200 miles by riding bike for 11 days and by running for 15 days.

Answer 2

To determine the number of days, we need to set up equations relating the given values above. The total distance that Kayla would want to travel is a sum of the total distance she traveled from running and the total distance she traveled from biking. So,

200 miles = (6 miles/day) x + (10 miles/day) y

where x is the number of days she spent running and y is the number of days she spent biking.

If the minimum days she used for biking would be 15 days or y = 15, then

200 miles = (6 miles/day) x + (10 miles/day) (15 days)

Solving for x,
200 = 6x + 150
50 = 6x
x = 8.3333 days

Total number of days = 15 days for biking + 8.3333 days for running = 23.3333 days or about 24 days.