Question 669703
if i did this correctly, they should be able to talk for 3.74 hours.
first of all, lauren drives for 1/2 hour before jeff starts.
70 mph for 1/3 hour is equal to 35 miles.
then jeff starts.
once jess starts, they will both be driving for the same time.
the total distance they need to travel to be 440 miles apart is now only an additional 405 miles since lauren is already 35 miles away.
the formula is rate * time  = distance.
the distance that jeff travels is equal to his rate * the mutual time which is called T.
his distance is therefore 55T
lauren's distance is therefore 70T
the total distance traveled by both has to equal 440 miles minus 35 miles = 405 miles.
the formula becomes 55T + 70T = 405
solve for T to get T = 3.24 hours.
you have to add the 1/2 hours that lauren was driving while jeff was just sitting there to get a total of 3.74 hours where they can still be in touch with each other.
after that, they're out of range.
the breakdown is as follows:
lauren drives for 35 miles before jeff even starts.
jeff drives at 55 miles per hour for 3.24 hours for a distance of 178.2 miles
lauren drives at 70 miles per hour for the same 3.24 hours for a distance of 226.8 miles.
jeff has gone 178.2 miles in one direction.
lauren has gone 226.8 + 35 = 261.8 miles in the other direction.
the total distance between them is 178.2 + 261.8 = 440 miles.


the answer to the question is that they will be able to talk on their cell phones for a total of 3.74 hours.