SOLUTION: Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving at 70 miles per hour. They drive in opposite directions, and Lauren has a half-hour head

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Question 1126950: Jeff starts driving at 65 miles per hour from the
same point that Lauren starts driving at 70
miles per hour. They drive in opposite
directions, and Lauren has a half-hour head
start. How long will they be able to talk on
their cell phones that have a 250-mile range?
Found 2 solutions by ankor@dixie-net.com, Theo:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving at 70 miles per hour.
They drive in opposite directions, and Lauren has a half-hour head start.
How long will they be able to talk on their cell phones that have a 250-mile range?
:
t = drive time of Jeff
then (half-hour = .5 hrs)
(t+.5) = drive time of Lauren
:
65t + 70(t+.5) = 250
65t + 70t + 35 = 250
135t = 250 - 35
135t = 215
t = 215/135
t = 1.59 hrs is Jeff's travel time
;
Assuming Jeff was talking with Laura during the half hour she alone was driving.
1.59 + .5 = 2.09 hrs which is 2 + .09(60) = 2 hrs 5 min
:
check
1.59(65) + 2.09(70) = 246.65 ~ 250

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i think it works this way.

jeff drives at 65 miles per hour from the same point that lauren drives at 65 miles per hour.

they drive in opposite directions.

lauren has a half hour head starts.

rate * time = distance.

for jeff, the equation becomes 65 * T = D

T is the time
D is the distance.

for lauren, the equation becomes 70 * (T + .5) = 250 - D

T + 5 means she drives a half hour more than jeff.

since they drive in opposite directions, the distance that each travels is additive.

you get D + 250 - D = 250.

250 is the total distance both travel.

since D = 65 * T and 250 - D = 70 * (T + .5), then you get:

65 * T + 70 * (T + .5) = 250

simplify to get 65 * T + 70 * T + 35 = 250

combine like terms to 135 * T + 35 = 250

subtract 35 from both sides of the equation to get 135 * T = 215

divide both side of the equation by 135 to get T = 215 / 135 = 1.592592593.

jeff traveled 65 miles per hour * that for a distance of 103.5185185 miles.

lauren traveled 70 miles per hour * (that + .5) for a distance of 146.4814815 miles.

add the miles up and they total 250 miles.

jeff traveled for 1.592592593 hours at 65 miles per hour.

lauren traveled for 1.592592593 + .5 = 2.092592593 hours at 70 miles per hour.

the questions was:

How long will they be able to talk on their cell phones that have a 250-mile range?

if you are talking about how long they can talk to each other on their cell phone after lauren starts driving, then that has to be 2.092592593 hours.

after that amount of time, their cell phones will be out of range of each other.