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.

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) (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:
.
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:
.
145*t = 370 - 35 = 335
.
Solve this equation by dividing both sides by 145 to find that:
.
t = 335/145 = 2.310 hours
.
which is about 2 hours and 19 minutes
RELATED QUESTIONS
Jeff starts driving at 75 miles per hour from the same point that Lauren starts driving... (answered by bucky)

jeff starts driving at 55 miles per hour from the same point that lauren starts driving... (answered by checkley71)

Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving... (answered by ankor@dixie-net.com,Theo)

Jeff starts driving 55 miles per hour from the same point that Lauren starts driving at... (answered by Alan3354)

Hello, I have this word problem that i could use some help on. Jeff starts driving... (answered by Paul)

Jeff starts driving at 55 miles per hour from the same point that lauren starts driving... (answered by mananth)

jeff starts driving at 60 mph from the same point that lauren starts driving 50 mph. they (answered by oberobic)

[ Jeff starts driving at 45 miles per hour from the same point that Lauren starts driving (answered by TimothyLamb)

Jeff starts driving at 55 mph from the same point that Lauren starts driving from 70 mph. (answered by checkley75)