Question

Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. This week, he spent more than 6 hours training for the race. Which graph represents his possible training times this week?

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the right of the line is shaded.

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the left of the line is shaded.

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the right of the line is shaded.

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the left of the line is shaded.

Answer 1

Let r = number of runs and s = number of swims. Total time 0.75r + 1.5s > 6. Divide by 0.75: r + 2s > 8.

The boundary r + 2s = 8 is the dashed line through (0,4) and (8,0). Because the inequality is “>” we shade the side r + 2s > 8 (to the right of that line). So the first graph is correct.