SOLUTION: Tom and Gary are leaving the same town for a meeting in different cities. However, they have not quite finished discussing a business plan. Tom must leave 1 1/2 hours earlier then

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Question 763339: Tom and Gary are leaving the same town for a meeting in different cities. However, they have not quite finished discussing a business plan. Tom must leave 1 1/2 hours earlier then Gary to make his meeting. Tom heads east on a train at 55 miles per hour. Gary heads west on a train at 70 miles per hour. How long can they talk on their phones if the phones have a range of 276.25 miles?
Answer by ramkikk66(644) (Show Source):
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Tom and Gary are leaving the same town for a meeting in different cities. However, they have not quite finished discussing a business plan. Tom must leave 1 1/2 hours earlier then Gary to make his meeting. Tom heads east on a train at 55 miles per hour. Gary heads west on a train at 70 miles per hour. How long can they talk on their phones if the phones have a range of 276.25 miles?
Answer:
Tom travels for 1.5 hours before Gary starts. In that time he travels 55*1.5 = 82.5 miles
After that, since they travel in opposite directions, the distance between them increases by (55+70) = 125 miles every hour.
Let us say than can talk for x hours before they go out of range.
Since the initial gap between them is 82.5, and it increases by 125 every hour, we have the equation

So they can talk for another hours or 1 hour and 33 minutes.
:)