Jason and Mary are running on 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 left to finish the race when Jason is on the finish line?
Correct answer: C. 12.5 meters
- A. 10.5 meters
- B. 11.5 meters
- C. 12.5 meters
- D. 13.5 meters
Explanation
We are given two expressions that represent the distance to the finish line for Jason and Mary at time t seconds:Jason: -8t + 200Mary: -7.5t + 200This means both runners start 200 meters away from the finish line, and their speeds are 8 m/s for Jason and 7.5 m/s for Mary.Step 1: When does Jason reach the finish line?To find that, we set Jason's distance to 0:-8t + 200 = 0 Add 8t to both sides: 200 = 8t Now divide by 8: t = 25So Jason finishes the race in 25 seconds.Step 2: How far is Mary at t = 25?Now plug t = 25 into Mary's expression:-7.5(25) + 200 = -187.5 + 200 = 12.5
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