SOLUTION: Hi, I would like to know if someone can help with this word problem? thanks. Jeff starts driving at 55mph from the same point that Lauren starts driving at 70mph. They drive in

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Question 669703: Hi, I would like to know if someone can help with this word problem? thanks.
Jeff starts driving at 55mph from the same point that Lauren starts driving at 70mph. 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 440 mile range?
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
What is Lauren's head start in miles?

mi
---------------
Start a stop watch when Jeff leaves
They will move apart for the same
amount of time until they are
440 mi apart
Let = the distance Jeff travels
in time
------------
Jeff's equation:

Lauren's equation:

--------------------
Substitute (1) into (2)

They can talk for 3 hrs 14 min 24 sec plus 1/2 hr
that is 3 hrs 44 min 24 sec
check:

and

OK