give two possible ways you can excersize

Question

you work out at least 10 hours a week, but no more than 15 hours a week. You divide your exercise time between swimming and running. This week, you want to spend at least twice the amount of time on swimming as on running. Write and graph a system of linear inequalities that gives the amounts of time you spend on each different kind of exercise. Then give two possible ways you can exercise

Answer 1

10 ≤ s + r ≤ 15

s ≥ 2r

 

Label the x-axis as swimming and the y as running.

 

To graph the first, start at (1,9), then (2,8), etc and connect them with a solid line. Then start at (1,14), then (2,13), etc and connect with another line. You should have two parallel lines. Shade everything in between (use vertical lines).

 

You should be able to graph the 2nd. Use a solid line and shade everything above it (use horizontal lines).

 

Pick any two points in the overlap for your answer. For example, (3,4) would be 3 hours running and 4 hours swimming.

 

 

Answer 2

R is the amount of time running

S is the amount of time swimming

 

------------ TEMPORARILY treating them as strict equations just for the sake of solving them ------

 

10 <= R + S <= 15

 

s = 2r

 

10 <= r + 2r <= 15

 

 

10 <= 3r <= 15

 

10/3 <= r <= 5

 

3 and 1/3 <= r <= 5

 

 

10 <= R+S <= 15

 

S >= 2R

 

Running             swimming          total

 

3 and 1/3               6 and 2/3                 10 

 

3 and 1/2 = 3.5        7                    10.5

 

4                              8                   12

 

4 and 1/2 = 4.5      9                   13.5

 

5                            10                 15

 

 

Between 3 hours and 20 minutes to 5 hours running.

Between 6 hours and 40 minutes to 10 hours swimming.