Question

Two jets leave an air base at the same time and travel in opposite directions. One jet travels 66 mi/h faster than the other. If the two jets are 7692 mi apart after 6 hours, what is the rate of each jet?

Answer 1

okay... so any ideas?

Answer 2

Well, I know we need to make a distance, rate, time table. We also need to find out what x and y will be...

Answer 3

mind telling me what the title of your unit is? there's a few ways to do this problem and I want to know which way you are supposed to do

Answer 4

The topic name is: Solving a distance, rate, time problem using a system of linear equations.

Answer 5

okay goodie. So, waht's the relationship between distance and rate?

Answer 6

If you multiply time and rate you get a distance.

Answer 7

Yup. So in the case of our jets, what exactly is the rate? first jet? second jet? both jets?

Answer 8

what do you think our variables should be?

Answer 9

Our variables should stand for the jets rates, I think...

Answer 10

Like x for the faster jet and y for the slower jet...

Answer 11

Hello?

Answer 12

omg sorry

Answer 13

and yes, that's correct. so what does x+y stand for?

Answer 14

It's okay. :)

Answer 15

Not sure..

Answer 16

x+y is the total rate right? jets are moving in different directions so the distance apart for time t is (x+y)t no?

Answer 17

I guess, I don't know I feel confused...

Answer 18

What do I write down for what x and y actually stand for?

Answer 19

What you said.
Like x for the faster jet and y for the slower jet...
faster jet's RATE.

Answer 20

they asked us to do rate, so let's set our variables as rate to make it easy right?

Answer 21

And if I were to make a table for this information, then what do I write under the rate column for each jet?

Answer 22

What are the columns of your table?

Answer 23

The columns are rate, time, and distance. And then the rows are faster jet and slower jet.

Answer 24

Okay. So, we just said rate of jets are x for faster and y for slower right?

Answer 25

Right.

Answer 26

Ok, what about time?

Answer 27

Time is 6 hours for both.

Answer 28

And distance?

Answer 29

Well, I guess for the faster jet it would be 6x and for the slower jet it would be 6y...

Answer 30

but that completes the tables. Let's move on to the equations...

Answer 31

So, we'll need 2 equations because we have 2 variables... any ideas?

Answer 32

Not really. I would say 6x = 7692 and 6y = 7692 but I think these are wrong.

Answer 33

Does it have something to do with the 66 mi/h?

Answer 34

oh... 7692 doesn't actually work LOL

Answer 35

so yes you were right regarding 6x and 6y :)

Answer 36

and, what do we know about the 66mi/h?

Answer 37

That it is a rate? >_<

Answer 38

is it? what did the problem say 66 mi/h was?

Answer 39

It is how much faster one of the jets is going compared to the slower one.

Answer 40

and how can we write that in math?

Answer 41

I'm guessing we need to multiply here??

Answer 42

Well, I was really just asking you to trasnlate your statement from an english sentence to a mathematical statement... in other words an equation expressing the relationships between how much faster the jets are going...

Answer 43

66x = y ??

Answer 44

and you said x and y are the rates of the jets right? you're saying here, the faster jet's speed multiplied by 66 is equal to the slower jet?

Answer 45

I guess. :/

Answer 46

Well, if it seems weird, fix it :P

Answer 47

That's incorrect, isn't it?

Answer 48

What was the original statement again?

Answer 49

I don't know what to fix it to.

Answer 50

No worries, let's start over from the statement. What's the sentence we're trying to translate?

Answer 51

The rate of 66 mi/h is how much faster one of the jets is going compared to the slower one.

Answer 52

How about just, One jet's rate is 66 mi/h more than another jet's rate?

Answer 53

Wanna try translating that one to math? :P

Answer 54

Is it supposed to be an equation?

Answer 55

We're turning this word problem into a math problem... we need 2 equations no? and we're using the information from the problem to get both?

Answer 56

Wait. I figured it out.

Answer 57

x + 66 = y ???

Answer 58

the faster jet's speed plus 66 mi/h equals the slower jet's speed?

Answer 59

** y + 66 = x

Answer 60

yup!. ok, one down, one more.

Answer 61

this equation... will probably use the rest of the information we have, right?

Answer 62

Right.

Answer 63

any ideas?

Answer 64

Well, as you just said, it's going to have something to do with the 7692 miles.

Answer 65

ok what is the significance of the 7692 miles?

Answer 66

It is how far the two jets are after 6 hours.

Answer 67

Can you translate that statement?

Answer 68

7692 = 6x + 6y ??

Answer 69

aha. yup.

Answer 70

And how do we solve this?

Answer 71

We can add the equations after we get y alone on one side?

Answer 72

Then figure out one of the variables.

Answer 73

well, that is the slow way :)

Answer 74

What other way is there?

Answer 75

OH WAIT

Answer 76

We can put (y + 66) into the equation for x...

Answer 77

yes...

Answer 78

let me know what you get for x and y

Answer 79

y = 608
x = 674

Answer 80

That's what I got :)

Answer 81

Thank you so much for all your help and sorry for being so clueless!

Answer 82

I just have one question left. :)

Answer 83

no problem - you weren't very clueless at all; most people wouldn't be able to steer themselves into the solution that easily...
I have to head to bed, but I'm sure you'll find someone to help you with for your next problem!
best wishes

Answer 84

Thanks! :)