SOLUTION: Jeff starts driving at 75 miles per hour from the same point that Lauren starts driving at 70 miles per hour. They drive in opposite directions, Lauren has a half-hour head start.

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Question 73763: Jeff starts driving at 75 miles per hour from the same point that Lauren starts driving at 70 miles per hour. They drive in opposite directions, Lauren has a half-hour head start. How long will they be able to talk on their cell phones that have a 370-mile range?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let t be the time that Jeff drives. Then the time that Lauren drives is t + 1/2 hour.
.
The basic equation we will be using is Distance = Rate * Time
.
The distance Lauren covers has a rate of 70 mph and a time of (t + 1/2) so her distance is
.
D = r*t = 70*(t + 1/2) = 70*t + 35
.
Jeff drives for time t at a rate of 75 mph. So Jeff's distance is:
.
D = r*t = 75*t
.
When the sum of these two distances equals 370 miles, Jeff and Lauren's cell phones will
stop operating. So we can set up the equation:
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70*t + 35 + 75t = 370
.
Adding the terms containing t results in:
.
145*t + 35 = 370
.
Eliminate the 35 on the left side by subtracting 35 from both sides to get:
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145*t = 370 - 35 = 335
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Solve this equation by dividing both sides by 145 to find that:
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t = 335/145 = 2.310 hours
.
which is about 2 hours and 19 minutes