Question

Distance to Finish Line

(meters)
Jasen
-8t+200
Mary
-7.5t+ 200

Jason and Mary are running an a 200 meter track.
The expressions in the table above show the
distance to the finish line t seconds after they
started the race. How many meters will Mary have
Ieft to finish the race when Jason is on the finish
line?
​

Answer 1

12.5 meters

Step-by-step explanation:

Given

`J(t) = -8t + 200` --- Jasen

`M(t) = -7.5t + 200` --- Mary

Required

Determine the number of metres left for Mary when Jason finishes

When Jasen finishes the race;

`J(t) = 0` -- Because Jasen is already at the stoppage

So, we need to calculate time spent by Jasen to get to the finished line.

`J(t) = -8t + 200`

Substitute 0 for J(t)

`0 = -8t + 200`

Collect like terms

`8t = 200`

Solve for t

`t = (200)/(8)`

`t = 25`

What this implies is that: we want to get Mary's distance at time;
`t = 25`

Substitute 25 for t in
`M(t) = -7.5t + 200`

`M(25) = -7.5 * 25 + 200`

`M(25) = -187.5 + 200`

`M(25) = 12.5`

Hence, Mary has 12.5 metres left