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Answer: A: 4.5 hours

B: No, she won't catch up.

C: 21 miles/hour

IMPORTANT: Please don't just copy the answers from the top and read all the sections down below! You can always learn something new.

Step-by-step explanation (SHOULD READ):

Hello! I hope this will help:

Hector = H

Wanda = W

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Distance of race = 42miles

[tex]V_{H} = 12miles/hour\\D_{H} = 42miles-18miles=24miles\\V_{W} = 16miles/hour\\D_{W} = 42 miles[/tex]

Vh = Velocity of Hector

Dh = Hector's distance to travel

Vw = Velocity of Wanda

Dw = Wanda's distance to travel

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Now, let's solve these exercises!

Write and solve an equation to find when Wanda will catch up to Hector.

The key words are the bolded words!

What do we have to find?

When Wanda..... Here we can see one thing: time

The word when indicates that we gotta find t (time).

catch up to Hector....

catch up indicates the fact that Wanda's position will be equal to Hector's position (Pos Hector = Pos Wanda)

And to Hector indicates position. Hector's position

So, at point A we gotta find the time that it would take for Wanda to catch up to Hector.

Wanda's speed (velocity) is greater (higher) than Hector's. Which means, after a definite amount of time, Wanda will catch up to him.

How to find the time it would take for Wanda to catch up to Hector?

Well, we gotta solve for time. We know their velocities, and their distance from eachother.

As we know, the formula for velocity is [tex]V=\frac{d}{t}[/tex]

That is Velocity = Distance divided by time.

We know: Distance, Velocity

So, we need to find the difference between our velocities. That way, we can know how faster you are than him, and in this case, Wanda than Hector.

Vwanda-Vhector = 16miles/hour-12miles/hour

The difference between their velocities is 4miles/hour.

That only means, that Wanda, every hour will walk 4 more miles, than Hector, because she's faster, obviously.

Velocity is 4miles/hour.

The distance will be the distance between the 2 children. That's 18 miles.

V = d/t

4miles/hour = 18miles/t

Let's calculate for t.

Multiply t on both sides.

4miles/hour * t = 18 miles * t / t

the time on the right side cancels out.

4 miles/hour * t = 18 miles.

divide 4 miles/hour on both sides.

4miles/hour * t / 4miles/hour = 18 miles / 4 miles/hour

the 4 miles/hour cancels out on the left side.

t = 18 miles / 4 miles/hour

the miles cancel out, remaining just the hour on the right side.

t = 18/4hours

t = 4.5 hours

If Wanda would travel for 4.5 hours, she will catch up to Hector!

And just like that, we solve A.

Let's move on B, shall we ?

The question is: Will Wanda catch up to Hector before the race is complete? Explain.

Pretty easy.

So, the question asks if Wanda has enough time to catch Hector, before he actually wins.

We know that Wanda's time to catch Hector = 4.5 hours.

What we need to do?

We need to calculate the time it will take Hector to finish the race, and then we'll go to the next step.

Hector's distance to finish the race = 42 miles - 18 miles = 24 miles.

Hector has to go 24 more miles to win.

His velocity is equal to 12 miles/hour.

V = d/t

12 miles/hour = 24 miles / t

multiply t on both sides, and the t on the right side will cancel out.

12 miles/hour * t = 24 miles * t / t

12 miles/hour * t = 24 miles

divide 12 miles/hour on both sides, and on the left side it will cancel out.

12 miles/hour * t / 12 miles/hour = 24 miles / 12 miles/hour

t = 24 miles / 12 miles/hour

The miles will cancel out, on the right side.

t = 24 / 12 hours

t = 2 hours

Now , to finish point B:

Her distance =  42 miles

Her velocity = 16 miles/hour

Time = Distance/Velocity

Her time = 42 miles / 16 miles/hour

the miles will cancel out on the right side

Her time = 42 / 16 hours

Her time = 2.625 hours to reach the finish.

Let's quickly display their times :

Hector : 2 hours

Wanda : 2.625 hours

Wanda did not have enough time to finish.

Hector finished the race in 2 hours, and Wanda in 2,6 hours (aproximately) .

Question: At what constant speed could Wanda travel to catch up with Hector at the finish line? Explain (boring)

At what velocity could Wanda travel at, to catch up Hector and win? That's the question.

Velocity of Hector = 12 miles/hour

Distance of Hector = 24 miles

Time of Hector = 2 hours

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Velocity of Wanda = ? (The enough velocity to pass Hector)

Distance of Wanda = 42 miles

Time of Wanda  = ? (It isn't 2.6hours because if Wanda walks faster she would have a smaller time)

Wanda's time = Hector's time, because we want to get at the finish exactly when Hector is at it.

Wanda's time = 2 hours

V = d/t

V = 42/2

V = 21 miles/hour

Just like that.

If Wanda would travel on her bike with 21 miles/hour she would've cought up to her friend.

Hi again! I really hope I helped you and I hope I didn't make any mistake, altough I don't I did. Succes!

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