Question

Alina is able to swim at a rate of about 2.5 miles per hour. Talia is able to swim at a rate of 1.8 meters per second. Which statement comparing the two swimmers is accurate?

Answer 1

do you have options that we can choose from?

Answer 2

1 mile 1,609 meters

Alina swims about 0.7 miles per hour faster than Talia.
Talia swims about 0.7 miles per hour faster than Alina.
Alina swims about 1.5 miles per hour faster than Talia.
Talia swims about 1.5 miles per hour faster than Alina.

Answer 3

Well, all your answers are in miles per hour, which means you need to convert Talia's swimming rate to miles. After that, you should be able to find the difference between their swimming rate by subtraction alone.

Answer 4

According to Google,\[1\text{ mile }=1609.344\text{ meters }\]

Answer 5

im just very confussed. i dont understand anythind

Answer 6

So Talia swims about 1.8 meters per second.
Two things to convert, then. Let's do one at a time.

Answer 7

Does it make sense, what I'm saying? If not we can start over :)

Answer 8

not really

Answer 9

Okay. Where are you confused? Let's go from there :)

Answer 10

well im in grade 9 and have iep . i dont understand anything

Answer 11

It's okay. Do you have any thoughts on the question that might help me point you in the right direction?

Anything counts. No wrong answers, just working out where to begin :)

Answer 12

well how do i try to figure the first thing out

Answer 13

Alright. Let's first understand the information we're given:
"Alina is able to swim at a rate of about 2.5 miles per hour" -- Alina swims at \(2.5\text{ miles/hour}\)
"Talia is able to swim at a rate of about 1.8 meters per second" -- Talia swims at \(1.8\text{ meters/second}\)

Answer 14

Good so far?

Answer 15

yeah

Answer 16

what do i do now

Answer 17

So we have your list of answers but they're all in "miles/hour" format. Talia's swimming rate is "meters/second" so we have to convert her rate to match the format given for your answer choices...

Since both top and bottom units need to be converted, we do one at a time.
(Technically you can do all at once, but that could be confusing to handle at first. So let's do one at a time)

Let's first convert Talia's "meters" part to "miles." One mile has 1609.344 meters, but decimals make things difficult so let's round down to 1609 meters. This means:\[\frac{1.8\text{ meters}}{1\text{ second}}\times\frac{1\text{ mile}}{1609\text{ meters}}\]
Are you with me so far?

Answer 18

i am with you

Answer 19

are you sill there

Answer 20

Yes, sorry. My internet is being a little slow.

Answer 21

thats ok

Answer 22

Talia swims about 1.5miles per hrfaster then Alina

Answer 23

@generation2006 Please don't give direct answers. :(

Answer 24

Also I have to verify if that's correct anyway xD

Answer 25

o ok sorry im new

Answer 26

It's okay, I'm not mad :)

Answer 27

Alright let me check my notes because I forgot where I was with all the lag --

Answer 28

thank you guys very much

Answer 29

ya sorry for spoiling the answer :(

Answer 30

Alright so we were here:
"Let's first convert Talia's "meters" part to "miles." One mile has 1609.344 meters, but decimals make things difficult so let's round down to 1609 meters. This means:\[\frac{1.8\text{ meters}}{1\text{ second}}\times\frac{1\text{ mile}}{1609\text{ meters}}\]

Okay, so you know how you can cross out stuff to simplify in algebra? In unit conversion it's pretty much the same thing, except that the units cancel out. So here, it'd be like this:\[\frac{1.8\cancel{\text{ meters}}}{1\text{ second}}\times\frac{1\text{ mile}}{1609\cancel{\text{ meters}}}\]And now you have this result:\[\frac{1.8}{1\text{ second}}\times\frac{1\text{ mile}}{1609}=\frac{1.8\times1\text{ mile}}{1\text{ second}\times1609}=\frac{1.8\text{ miles}}{1609\text{ seconds}}\]

Answer 31

Does this make sense so far?

Answer 32

@bloodywolf1 Everything alright?

Answer 33

Well, I'll just keep going for when you get back then. Let me know if anything gets confusing...

So now we have 1.8 miles per 1609 seconds. But this isn't the final rate so we're gonna keep converting the units, and simplify the number values later.
Now we know that there are 3600 seconds in one hour, so:\[\frac{1.8\text{ miles}}{1609\text{ seconds}}\times\frac{3600\text{ seconds}}{1\text{ hour}}\]And we cancel out the relevant units:\[\frac{1.8\text{ miles}}{1609\cancel{\text{ seconds}}}\times\frac{3600\cancel{\text{ seconds}}}{1\text{ hour}}=\frac{1.8\text{ miles}\times3600}{1609\times1\text{ hour}}=\frac{(1.8\times3600)\text{ miles}}{1609\text{ hours}}\]

Answer 34

At this rate I'd recommend using a calculator, or you could round up the denominator. But let's just work through the original equation here.
So \(1.8\times3600=6480\), which means we now have\[\frac{6480\text{ miles}}{1609\text{ hours}}\]To simplify, just divide this (ignoring the units for now): \[6480\div1609\approx4.027\rightarrow4.027\text{ miles/hour}\]So Talia swims at about \(4.03\) miles per hour.

Answer 35

yeah im alright . sorry

Answer 36

Now let's compare this to Alina's 2.5 miles per hour. We can see that Talia swims significantly faster, so we can cross out some choices:

Answer 37

its the bottom one

Answer 38

Now all we need to do is find the difference between Talia's swimming rate and Alina's swimming rate.

To do this, we will subtract Alina's rate from Talia's:\[4.03\text{ miles/hour}-2.5\text{ miles/hour}\approx4.0-2.5\text{ miles/hour}\rightarrow1.5\text{ miles/hour}\]Yeah, that's it. Just writing out all the steps for reference :)

Answer 39

Everything make sense? I can re-explain if necessary :)

Answer 40

thank you

Answer 41

Np :)