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!
A.
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 ?
B.
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) .
C.
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!
