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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?
​

Sagot :

MrRoyalidn

Answer:

12.5 meters

Explanation:

Given

[tex]J(t) = -8t + 200[/tex] --- Jasen

[tex]M(t) = -7.5t + 200[/tex] --- Mary

Required

Determine the number of metres left for Mary when Jason finishes

When Jasen finishes the race;

[tex]J(t) = 0[/tex] -- Because Jasen is already at the stoppage

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

[tex]J(t) = -8t + 200[/tex]

Substitute 0 for J(t)

[tex]0 = -8t + 200[/tex]

Collect like terms

[tex]8t = 200[/tex]

Solve for t

[tex]t = \frac{200}{8}[/tex]

[tex]t = 25[/tex]

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

Substitute 25 for t in [tex]M(t) = -7.5t + 200[/tex]

[tex]M(25) = -7.5 * 25 + 200[/tex]

[tex]M(25) = -187.5 + 200[/tex]

[tex]M(25) = 12.5[/tex]

Hence, Mary has 12.5 metres left

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