ALgebra 2 HELP!?

Question

Two sisters who live 500 miles apart decide to meet at the halfway point for a visit. Joanne leaves at 11 and travels 50 mph. At noon, Sue leaves travels at 60 mph. Who will reach the halfway point first, and how much longer will she have to wait for her sister?

I just need the basic set up equation. We have to make up our own equation and solve it. I'm not sure though on how to set it up.

Answer 1

The half way point is 250 miles.

Time = distance / speed

250 / 50 = 5 hours for Joanne who leaves at 11 and gets there at 4:00 PM
250 / 60 = 4 Hrs 10 minutes so Sue arrives at 4:10 PM, 10 minutes late as usual.

Joanne gets there first and waits 10 minutes for Sue.

if we let J be the time for Joanne and S is Sue's time then

using distance = speed x time
250= 50J = 60S

so your 2 equations are:

50J = 60S
S - J = 10/60

Answer 2

Joanne gets there at 4:00 ; Sue get there at 4:10, so Joanne has to wait 10 minutes.

Here is the working out of this :

Each travels 250 miles to reach the other.
The equations needed to solve this would be :

250 miles / 50 mph = 5 hours for Joanne
250 miles / 60 mph = 4 1/6 hours -- or 4 hours and 10 minutes for Sue
11am + 5 hours is 4 pm when Joanne arrives
12pm + 4 hours and 10 minutes is 4:10 pm when Sue arrives

So 4:10 - 4:00 = 10 minutes -- Joanne's wait time.

Answer 3

Joanne:
= ([250 / 50] + 11) - 12
= (5 + 11) - 12
= 16 - 12
= 4 PM

Sue:
= ([250 / 60] + 12) - 12
= (4:10 + 12) - 12
= 16:10 - 12
= 4:10 PM

Answer: Joanne arrives first and has to wait for Sue for 10 minutes.

Answer 4

Joanne: 250 miles at 50mph=250/5=5hrs to travel the 250 miles(which is the mid-point)
Since she left at 11am, she arrives at 4pm

Sue: 250 miles at 60mph =250/60= 41/6 hours
Since she left at noon, she arrives at 4:10pm (1/6 of an hour is 1/6 of 60 minutes, or 10 minutes)

Joanne arrives first, has to wait 10 minutes.

We could set up the equation as follows:
D=R x T, so T=D/R
T(j)=D(j)/R(j)
T(s)=D(s)/R(s)
Those are the basic set-up equations

Answer 5

for Joanne: 250 = 50x, x = time from 11:00
Sue: 250 = 60y, y = time from 12:00
solving for x and y will give you the times of arrival at the halfway point for each, and subtraction will give the wait time.

Answer 6

You know that both sisters have to travel the same distance - 250 miles.

You also know how fast each sister is travelling.

Using the equation speed = distance / time you should be able to work out how long it will take each sister to reach the halfway point, and how hence how long the 1st sister must wait.

Answer 7

that is easy but your going to have 2 different equations or just 1 long one try it this way first with the 2 diff equ. k dang you might need to give an equation for each varible [(y) (x)] just follow the setup i did but just make one equ. for (y) and the reason you are going to use (2) cause there are TWO sisters k.
1) 2x+50=500
2)2y-60=500