SOLUTION: Two brothers leave from the same point driving in opposite​ directions, the first brother driving at 45 miles per hour and the second at 60 mph. The first brother has a&#8203

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Question 1055676: Two brothers leave from the same point driving in opposite​ directions, the first brother driving at 45 miles per hour and the second at 60 mph. The first brother has a​ one-hour head start. If each brother has a communication device that allows him to talk to the other for up to a 200​-mile ​range, how long will they be able to talk to each​ other?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
                   SPEED       TIME       DISTANCE
POS                  45         t+1
NEG                  60          t
TOTAL                                      200


                   SPEED       TIME       DISTANCE
POS                  45         t+1       45(t+1)
NEG                  60          t         60t
TOTAL                                      200


You are looking for t+1.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Two brothers leave from the same point driving in opposite​ directions, the first brother driving at 45 miles per hour and the second at 60 mph. The first brother has a​ one-hour head start. If each brother has a communication device that allows him to talk to the other for up to a 200​-mile ​range, how long will they be able to talk to each​ other?
From the time the slower brother started travelling to the time both are 200 miles apart, they will be able to communicate

Therefore, let time 1st (slower) brother took to get 200 miles from 2nd brother be T

Then time 2nd (faster) brother took to get 200 miles from 1st brother is: T - 1

When they’re 200 miles apart, the slower and faster brothers would’ve traveled 45T and 60(T – 1), or 60T – 60 miles, respectively

We then get: 45T + 60T – 60 = 200

105T = 260

T, or time both can communicate = , or  

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