Question

Marco can run 3 miles per hour faster than Polo. Marco ran 12 miles in the same time it took Polo to run 8 miles.

Answer 1

I need to fill in a table for Marco and Polo's Distance, Rate, and Time. Then determine their speed.

Answer 2

@Hero

Answer 3

\(\begin{array}{|c|c|c|c|}
\hline
&\text{Distance}&\text{Rate}&\text{Time}\\
\hline
\text{Marco}&&&\\
\hline
\text{Polo}&&&\\
\hline
\text{Total}&&&
\hline
\end{array}\)

Answer 4

thats what it looks like on my paper

Answer 5

umm, so Marco is 12 and Polo is 8

Answer 6

Total is 20

Answer 7

So did they run the same time or different time?

Answer 8

it says for the different distances they ran the same time

Answer 9

Correct, they ran the same time so we'll let \(t\) represent the time for both runners:

\(\begin{array}{|c|c|c|c|}
\hline
&\text{Distance}&\text{Rate}&\text{Time}\\
\hline
\text{Marco}&12&&t\\
\hline
\text{Polo}&8&&t\\
\hline
\text{Total}&&&
\hline
\end{array}\)

Answer 10

Okay, so now all we have to do is figure out the rates for both. Who ran faster than whom?

Answer 11

Marco

Answer 12

uh, 3miles per hour faster than Polo

Answer 13

Good, so whatever Polo's speed is, Marco ran 3 miles per hour faster than that:

Answer 14

So if we let \(r\) represent Polo's speed, how can we show that Marco ran three miles per hour faster than that?

\(\begin{array}{|c|c|c|c|}
\hline
&\text{Distance}&\text{Rate}&\text{Time}\\
\hline
\text{Marco}&12&&t\\
\hline
\text{Polo}&8&r&t\\
\hline
\text{Total}&&&
\hline
\end{array}\)

Answer 15

r + 3?

Answer 16

Correct:
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Hero
So if we let \(r\) represent Polo's speed, how can we show that Marco ran three miles per hour faster than that?

\(\begin{array}{|c|c|c|c|}
\hline
&\text{Distance}&\text{Rate}&\text{Time}\\
\hline
\text{Marco}&12&r+3&t\\
\hline
\text{Polo}&8&r&t\\
\hline
\text{Total}&&&
\hline
\end{array}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 17

So how can we set up an equation to find \(r\)?

Answer 18

r = 8/t ?

Answer 19

We need to start off by setting two things that we know are equal, equal to each other.

Answer 20

And what would that be @Taco ?

Answer 21

the other rate?

Answer 22

What two things that we discussed earlier are same for both Marco and Polo?

Answer 23

oh time

Answer 24

I think I get it

Answer 25

Correct, they both ran the same length of time together so we set \(t = t\). Do you think you can set up the next step from here?

Answer 26

let me try

Answer 27

Post your steps here

Answer 28

You can use either the drawing board or the equation buttons located just below the text box.

Answer 29

12/(r +3) = 8/r
12r = 8(r +3)
12r = 8r +3
4r = 3
r = 3/4

is that right

Answer 30

12r = 8(r +3)

Can you try re-doing this step by distributing the 8 using the distributive property?
\(a(b + c) = ab + ac\)

Answer 31

oh

Answer 32

12r = 8(r +3)
12r = 8r + 24
4r = 24
r = 6

Answer 33

So what does the 6 represent in this case?

Answer 34

Polo runs 6mph ?

Answer 35

and Marco runs 9mph?

Answer 36

Correct.

Answer 37

oh wow

Answer 38

thank you I didnt understand this

Answer 39

Let's check by making sure the times are the same for both.

Answer 40

t = 8/6 = 4/3

t = 12/9 = 4/3

Answer 41

Very good. So they both ran about 1 + 1/3 hours. 6 miles or 9 miles in 1 + 1/3 hours. Seems a reasonable time for running mileages.

Answer 42

Can you help me with more?

Answer 43

Create a new post for the next question.

Answer 44

i don't see the text box

Answer 45

Because you have to close this question first.

Answer 46

oh