Question

Enter an equation that can be used to solve this problem, where x represents the number of hours that the first plane had been traveling.

Two planes left the same airport traveling in opposite directions. The first plane left the airport at 2 P.M. traveling at an average rate of 500 mph. The second plane left the airport at 4 P.M. traveling at an average rate of 550 mph. When will the planes be 3100 miles apart?

Enter the amount hours, after the first plane left, when the planes will be 3100 miles apart.
Equation:


2 h

Answer 1

do you know about
rate * time = distance
?

Answer 2

no XD

Answer 3

if you go 500 mph for 2 hours, any idea how far you went?

Answer 4

1000 miles

Answer 5

yes, you did 500*2

if you go for "x" hours you do the same thing:
500*x

Answer 6

oh

Answer 7

in other words,
The first plane left the airport at 2 P.M. traveling at an average rate of 500 mph for "x" hours

we don't know what x is (as a number) but we know the distance will be
500x

ok so far ?

Answer 8

mhm

Answer 9

distance is rate * time
rate (or speed) is 500 miles per hour
time is x (unknown) number of hours
the distance is
500*x or 500x (we usually leave out the multiply sign, but 500x means 500 * x)

Answer 10

I'm still with you not confused yet XD

Answer 11

the 2nd plane leaves two hours later
if the first plane flies for x hours, any idea how long the 2nd plane is flying ?

Answer 12

550 is how fast the next plane is flying

Answer 13

yes, but let's say the first plane flies for x hours and then we check how long the 2nd plane has been in the air (assuming it's still flying)
any idea how long the 2nd plane flew ?

Answer 14

let's use numbers
if the first plane has been flying for 3 hours, at that same time, how long has the 2nd plane been in the air?

Answer 15

it flew 1650

Answer 16

ok, but that is not the question.

if the first plane leaves at 2 pm and flies for 3 hours (so it's now 5 pm)
and the 2nd plane leaves at 4 pm, how long has the 2nd plane been flying ?

Answer 17

1h

Answer 18

if the first plane flies for 5 hours
how long will the 2nd plane be flying ?
any idea ?

Answer 19

2500

Answer 20

how many hours ?

Answer 21

5

Answer 22

5 hours for the first plane
how many hours for the 2nd plane ?

Answer 23

3

Answer 24

yes. how did you get 3?

Answer 25

you did 5 - 2

Answer 26

mhm

Answer 27

the idea is the 2nd plane flies 2 less hours because it leaves 2 hours later

Answer 28

so the second plan flies 1650

Answer 29

ok, but now we want to know how long it flies if the first plane flies for "x" hours

we use the idea that the 2nd plane flies 2 less hours or (x-2) hours.

Answer 30

next, we want the distance that the 2nd plane flies if it flies for (x-2) hours
how do we figure that out? we multiply the time (x-2) times the speed 550
can you do that ?

Answer 31

so we need to keep multipling to the second plane to figure it out ?

Answer 32

we use
rate * time to find the distance
rate (or speed) is 550
time is (x-2)

Answer 33

in other words, the distance the 2nd plane goes is 550(x-2)

Answer 34

mhm

Answer 35

the say the planes go in opposite directions, so the distance between them is the sum of how far each plane flies
distance = 500x + 550(x-2)

Answer 36

they want to know how many hours to get a distance of 3100 miles
3100 = 500x + 550(x-2)

that is the equation

Answer 37

i think i understand and the time is 3h

Answer 38

if we use x=3 in the formula
500x + 550(x-2)
we would get
500*3 + 550(3-2)
if we simplify that we get
1500+ 550*1 or 2050
that is not far enough

Answer 39

oh ok thanks !

Answer 40

we can use algebra to "solve for x" in the formula
500x + 550(x-2) = 3100

I would first "distribute" the 550
and do 550*x and 550*-2

500x + 550x -1100= 3100

next add 500 x's plus 550 more x's. that is 1050 x's or 1050x
1050x -1100 = 3100

now add +1100 to both sides.

Answer 41

2150

Answer 42

you should get
1050x = 3100+1100
or
1050x = 4200

finally, divide both sides by 1050

Answer 43

1050 for the left side gives you 1 and on the right gives 4

Answer 44

almost. 1050x/1050 is 1x or x
don't ignore the letters.

x= 4
is the answer
it takes 4 hours for the two planes to get 3100 miles apart.

Answer 45

ahh

Answer 46

thank you and bye XD