Question

Jack is running a 5-mile race with Jill. The distance he travels in miles versus the minutes he runs is represented by the function d=0.05t. Her run is represented by d=0.04t+0.5. What effect would be seen on Jill's starting point and speed, as compared to Jack's speed and starting point?

Answer 1

Hm.. distance, d = 5 mi. youre given both equations so you could find the time for each person.

Then use \(d= vt\implies v = \frac{d}{t}\) to compare the velocities.

Answer 2

\[5 \ mi=0.05t_1 \implies t_1 = \frac{5 \ \ mi}{0.05\ \ mpm} =100 \ \ min\]\[5 \ mi= 0.04t_2 +0.5 \implies t_2 =\frac{5 \ mi-0.5}{0.04 \ mpm} = 112.5 \ min\]

Answer 3

So now you just compare the velocities of both. \[v=\frac{d}{t}\]\[v_1 = \frac{5 \ mi}{100 \ min} = 0.05 \ mpm\]\[v_2 = \frac{5 \ mi}{112.5 \ mpm} = 0.04 \ mpm\]