Question 818711: [ Jeff starts driving at 45 miles per hour from the same point that Lauren starts driving at 40 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 [2-way radios], which have a 370 mile range? ]
NOTE: cell phones don't communicate phone-to-phone, but rather through the mobile networks via cell towers, so the idea of two cell phones might go out of range from each other is wrong and misleading, so I changed the problem to radios, which is conceptually what the original problem intended.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! Lauren's head start:
s = d / t
d = s * t
d = 40 * 0.5
d = 20 miles
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after Jeff starts driving we can simplify the problem to a single car at the two-car relative speed:
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s = 45 + 40
s = 85 mph
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after Jeff starts driving they will lose radio contact with each other at this relative-driven distance:
r = 370 - 20
r = 350 miles
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t = d / s
t = 350 / 85
t = 4.1176471 hours
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answer:
they will lose radio contact with each other:
4 hours, 7 minutes, 3.5 seconds after Jeff starts driving, or
4 hours, 37 minutes, 3.5 seconds after Lauren starts driving
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