Jose walks at a rate of 4 miles per hour and runs at a rate of 8 miles per hour. Each week, his exercise program requires him to cover a total distance of 20 miles with some combination of walking and/or running. Write an equation that represents the different amounts of time Jose can walk, x, and run, y, each week

Here we can use the relationship:

Distance = time*speed.

When Jose walks, his speed is 4 mph.

Then if he walks for X hours, the distance that he will travel is:

D = 4mph*X

When Jose runs, his speed is 8mph.

Then if he runs for T hours, the distance that he will travel is:

D´ = 8mph*Y

And we know that he travels in total 20 miles, then we must have that:

D + D´= 20mi

This leads to:

4mph*X + 8mph*Y = 20mi

Where X is the time that he walked, and Y is the time that he runed.

Then the equation that represents the different amounts of times that Jose runs and walks  is:

4mph*X + 8mph*Y = 20mi

Where we can not really find the solutions for Y and X, because there is only one equation and two variables.

i believe the correct answer is b.