Question

PLEASE HELP IM SO CONFUSED
write an equation to solve each problem

1.)two buses leave Houston at the same time and travel opposite directions. one bus averages 55mi/h and the other bus averages 45mi/h. when well they be 400 mi apart?

2.) two planes left an airport at noon. one flew east and the other flew west at twice the speed. After 3 hours the planes were 2700 miles apart. how fast was each plane flying?

Answer 1

Divide 400 by 55. That will be your total hours. Use the units to cancel out to solve for what you want, hrs. So you are trying to solve for hours, given miles, \(400\frac{mi}{1} \times \frac{h}{55~mi}\) So you notice that the miles cancel out! And you
re left with \(\frac{400}{55} h\) Upon dividing, you get 4 hours.

Answer 2

What? when you divide 400 by 55 you get 7.272...

Answer 3

@abb0t

Answer 4

Oh i get it!!! you add the 45 and 55 than divide!

Answer 5

because they are two different buses and when you add they equal 100 than you take 400/100 and get 4 hours like what you said...

Answer 6

Well, I just divide each one individually, 400 divided by 55 = 4

Answer 7

\(\begin{matrix}
&distance& rate & time\\
1st\ bus& x & 55 & t\\
\hline\\
2nd\ bus&400-x&45&t
\end{matrix}\)

Answer 8

400 divided by 55 = 7.272727273, check your calculator again

Answer 9

see the equations?

Answer 10

when they both reach 400 miles apart, their time is the same, thus the time for 1st bus = time for 2nd bus

Answer 11

oh, wait, you're right. Lol. i did this in my head. LOL. i was getting 200 for some reason.

Answer 12

how far has 1st bus traveled? we dunno, thus "x"
how far has 2nd bus traveled? well, if trhe 1st bust traveled "x", the 2nd one traveled 400-x

Answer 13

ok so how do we find x

Answer 14

how would i make one equation with that info

Answer 15

\(\begin{matrix}
&distance& rate & time\\
1st\ bus& x & 55 & t\\
\hline\\
2nd\ bus&400-x&45&t\\
\hline\\ \hline\\
\textit{distance = rate } \times \textit{time}\\
\bf x = 55t\\
\bf 400-x = 45t
\end{matrix}\)

Answer 16

notice that x= 55t on 1st of the system of equations
since we know that now then, use that value of "x" in the 2nd equation, what do you get?

Answer 17

you would add 55t on both sides and get 100t than divide by 100 on both sides and get t= 4 hours

Answer 18

:)

Answer 19

thank you so much! i can do this for the second one too :)

Answer 20

yeah, the 2nd is pretty much the same thing

Answer 21

with the second one would the equation be 2700=3x+2x(3) or???

Answer 22

yeap

Answer 23

yay!! i got it thank you :)

Answer 24

yw