The Race Between Two Friends

Question

Yourry and Timothy are competing against each other in the regional track meet to determine who will move on to the championship of the 100-meter dash. Yourry's distance covered, in meters, after t seconds can be modeled by the equation h(t)=sqrt(200t+1707). Timothy's progress is modeled by the equation h(t)=sqrt(300t+793)

Who gets to the finish line first? At what time does Yourry or Timothy finish the race? Explain

Answer 1

Hello Sa'veon! Thanks for your question.

Yourry and Timothy are competing for the 100 meter dash. That means they will each be running 100 m. Since each equation represents the number of meters covered in t seconds, h(t) = 100. To determine who wins the race, you need to find out how many seconds (t) it takes each of them to reach 100 m.

For Yourry: h(t) = sqrt(200t +1707)

100= sqrt(200t +1707), square both sides

10,000 = 200t + 1707, subtract 1707 from both sides

8293 = 200t, divide both sides by 200

41.5 = t

It takes 41.2 seconds for Yourry to run 100 m.

For Timothy: h(t)=sqrt(300t+793)

100= sqrt (300t + 793), square both sides

10,000 = 300t + 793, subtract 793 from both sides

9207= 300t, divide both sides by 300

30.7 = t

It takes Timothy 30.7 seconds to run 100 m.

Therefore, Timothy wins the race, running the 100 m dash in 30.7 seconds. Yourry takes 41.2 seconds to run the 100 m dash.

Answer 2

Since the race is 100 meter dash, we can let h(t)=100 meters. So we will set both equations equal to 100 and solve them for t to find out who finishes first:

Yourry:

100= √(200t+1707)

square both sides to get rid of the square root:

10,000 = 200t +1707

Subtract 1707 from both sides:

8293 = 200t

Divide both sides by 200

t= 41.465 seconds

Timothy:

100= √(300t+793)

Square both sides to get rid of the square root:

10000= 300t + 793

Subtract 793 from both sides:

9207 = 300t

Divide both sides by 300:

t= 30.69 seconds

So Timothy reaches the finish line first and it takes him 30.69 seconds.

Answer 3

Finding how long it takes Yourry to cross the finish line is simply setting h(t)=100 and solving for t. Do this for Timothy's progress function as well and compare the two answers.