Can someone help me set up this up? word problem into equation?

[sarahfryeclark]

Hi, I'm having some trouble setting up the following word problem. My professor recommends using a table to organize what we know and then using that info to solve. I just cant seem to get everything into the table so that i can try to solve. The problem is below:

Two buses leave Smithville at the same time, one traveling north and the other traveling south. The northbound bus travels at 50 mph and the southbound bus travels at 65 mph. When will the two buses be 345 apart?

The table is set up like this:
rate time distance
north 50 x 50x

south 65 x-??? 65(x-??)

we would then have 50x + 65(x-??) = 345 then i could solve for x. i just cant figure out what I'm missing.

thanks for your time

 

[HallsofIvy]

Hi, I'm having some trouble setting up the following word problem. My professor recommends using a table to organize what we know and then using that info to solve. I just cant seem to get everything into the table so that i can try to solve. The problem is below:

Two buses leave Smithville at the same time, one traveling north and the other traveling south. The northbound bus travels at 50 mph and the southbound bus travels at 65 mph. When will the two buses be 345 apart?

The table is set up like this:
rate time distance
north 50 x 50x

south 65 x-??? 65(x-??)

we would then have 50x + 65(x-??) = 345 then i could solve for x. i just cant figure out what I'm missing.

thanks for your time

I have no idea what your "??" means! What did you intend to mean? You say "x" is "time". Okay, time from what? (The answer lies in the fact that you have just "x" itself in "north 50 x 50x" [once you have explained to yourself what you meant when you wrote it!]). The important fact, that you have not used, is that the "Two buses leave Smithville at the same time".

 

[ahspadafora]

here is a table to help

	R	D	T
NB bus	50mph	x	y
SB bus	65 mph	345-x	y

Okay so you want to solve for the time it takes to get 345 miles apart, and the distance each individual bus gets right?

Now we know the distance is 345 - x miles for one of the buses & x for the other because the distance of NB bus + the distance of the SB bus = 345 miles ( it doesn't matter which bus you make x and which one you make (345-x) )

We do not know the time it will take so lets make that y for both buses

We know that Rate * Time = Distance

So for the NB BUS :

50y = x

and for the SB BUS 65y= 345 - x

now you want to isolate either x or y from that 2nd equation, that way you can solve the system of equations by substitution

65y-345= -x

divide by -1

-65y+345=x

substitue (-65y+345) for x in the first equation

50y=x
50y= -65y+345

add 65y to both sides

115y = 345

divide by 115

y = 3

CHECK YOUR SOLUTION

50y=x
50(3)=x
x=150

65y=345-x
65(3) = 345-x
195=345-x
x=345-195
x=150

the answer checks out.

the interpretation of y= 3 x= 150 is

In three hours the north bound bus and the south bound bus will be 345 miles apart.
Because in three hours the North Bound bus will have traveled 150 miles and the South Bound bus will have traveled 195 miles.

 

[lookagain]

ahspadafora, here are a few pointers:

1) You shouldn't work out a full solution for the student, as least in near time to the post of the OP.

2) You should try to help that student with the route he/she was already taking, such as HallsofIvy addressed.

3) You should not make the solution more complicated as you did with the introduction of another

variable, and on top of that combined with a less straight-forward equation.



---------------------------------------------------------------------
---------------------------------------------------------------------


sarahfryeclark, this is a tweak of your chart and your equation. Would you solve it now?



Let x = the time that both buses were traveling (Both buses traveled for the same amount of time.)



\(\displaystyle vehicle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ rate \ (mph) \ \ \ \cdot \ \ \ \ time \ (hours) \ \ \ = \ \ \ distance \ (miles)\)
-------------------------------------------------------------------------

northbound bus \(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 50 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 50x \)


southbound bus \(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 65 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 65x \)

_______________________________________________________________



50x + 65x = 345



Continue...

 

[sarahfryeclark]

Thank you everyone for your help. 50x + 65x= 115x=345 x=3
I appreciate it.
HallsOfIvy- i had inserted the question marks to show the info i didn't know. I apologize if I made it more confusing.
Thank you again.

ahspadafora, here are a few pointers:

1) You shouldn't work out a full solution for the student, as least in near time to the post of the OP.

2) You should try to help that student with the route he/she was already taking, such as HallsofIvy addressed.

3) You should not make the solution more complicated as you did with the introduction of another

variable, and on top of that combined with a less straight-forward equation.



---------------------------------------------------------------------
---------------------------------------------------------------------


sarahfryeclark, this is a tweak of your chart and your equation. Would you solve it now?



Let x = the time that both buses were traveling (Both buses traveled for the same amount of time.)



\(\displaystyle vehicle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ rate \ (mph) \ \ \ \cdot \ \ \ \ time \ (hours) \ \ \ = \ \ \ distance \ (miles)\)
-------------------------------------------------------------------------

northbound bus \(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 50 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 50x \)


southbound bus \(\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 65 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 65x \)

_______________________________________________________________



50x + 65x = 345



Continue...

 

[lookagain]

Thank you everyone for your help. 50x + 65x= 115x=345 x=3
Thank you again.

sarahfryeclark, please do not put together a chain of equations using equals sign.


Look at this instead:


50x + 65x = 345 \(\displaystyle \ \) ==>\(\displaystyle \ \) 115x = 345 \(\displaystyle \ \) ==> \(\displaystyle \ \) x = 3


------------------------------------------------------------


Better:


\(\displaystyle 50x + 65x = 345 \ \implies\)

\(\displaystyle 115x = 345 \ \implies \)

\(\displaystyle x = 3 \)


-----------------------------------------------------------


Or more simply in the usual style as:


50x + 65x = 345

115x = 345

x = 3