Ryan and janelle are each driving from a different location to meet. when they each stopped for lunch at 12 noon, they called each other on their cell phones. ryan had traveled 245 miles in 3 1/2 hours. janelle had driven 260 miles in 4 hours. if ryan and janelle were originally 910 miles apart when they had started driving that morning, at what time will they meet?

They will meet at 3:00 p.m.

Since Ryan traveled 245 miles in 3.5 hours, he traveled at a speed of 245/3.5=70 mph.  Janelle traveled 260 miles in 4 hours; she traveled at a speed of 260/4=65 mph.

Together, they had traveled 245+260=505 miles by noon.  This leaves 910-505=405 miles to travel.

If Ryan stays at a constant rate of 70 mph, his distance is given by 70t.  If Janelle stays at a constant rate of 65 mph, her distance is given by 65t.  Their distances together equal 405:
70t+65t = 405

Combining like terms, 

135t = 405

Divide both sides by 135:
135t/135 = 405/135
t = 3

3 hours after noon will be 3:00 p.m.