Answer:
a) 160 meters short
b) d = 200x +80y
c) (run, walk) = (2, 15), (4, 10), (6, 5)
d) see attached
Explanation:
You're being asked to write an equation describing the gym class requirement, and to find several values of the variables that satisfy the equation.
It is convenient to write the equation first (part b).
__
b)
At 200 meters per minute, in x minutes, Eric will run 200x meters. At 80 meters per minute, Eric will walk 80y meters in y minutes. His total distance covered will be ...
d = 200x +80y
__
a)
In the given times, Eric's distance covered is ...
d = 200(4) +80(8) = 800 +640 = 1440 . . . meters
Eric is 160 meters short of the 1600-meter goal.
__
c)
It is convenient to simplify the equation to one that lets us find one value in terms of the other.
200x +80y = 1600
5x +2y = 40 . . . . . . . . divide by 40
This will have integer solutions for even values of x in the range 0 to 8.
y = (40 -5x)/2
For x={2, 4, 6}, we have ...
y = (40 -5{2, 4, 6})/2 = {30, 20, 10}/2 = {15, 10, 5}
Eric can cover 1600 meters in (run, walk) times of ...
(run, walk) = (2, 15), (4, 10), (6, 5)
__
d)
The graph is attached. We'll let you read as many values from it as you may wish.