Please help algebra 1

Question

Gary and Alex live different distances from their school. They both leave home at the same time. Gary bicycles to school. His distance from the school in miles,d, as a function of t, time in minutes, is given by this equation.

d=-1/5t+5

Alex skateboards to school. The table shows his distance from school at different times.

(Alex skateboards to school) Time since leaving home in minutes and Distance from school in miles

6 and 2.5

12 and 2.0

18 and 1.5

which boy arrives at school first? how many minutes before the other boy arrives? Show your work.

(Answer only)

Answer 1

Gary arrives at school after 25 minutes. Set the equation with d = 0, and solve for t, giving 25.

To calculate Alex's time, it's necessary to assume that his velocity remains constant after the time given.

It is constant during the time listed on the chart, as his distance from the school decreases by 0.5 miles every 6 minutes. Extrapolating would require another 1.5 miles to be lost, which would occur in 18 more minutes.

(That can be determined by setting up an equation in proportion such as x/1.5 = 6/0.5, and x = 18. Also graphing could give this result. Or one could simply extend the chart with several more entries at intervals of 6 minutes, and stopping when the distance is 0). In any event, add these additional 18 minutes to the 18 already taken, and the total time for Alex is 36 minutes. It takes Alex 36 - 25 = 11 minutes after Gary.