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:
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

{{{82.5 + 125*x = 276.25}}}

{{{125*x = 193.75}}}

{{{x = 193.75/125 = 1.55}}}

So they can talk for another {{{highlight(1.55)}}} hours or 1 hour and 33 minutes.

:)