At 1:00 p.m. a car leaves st. louis for chicago, traveling at a constant speed of 65 miles per hour. at 2:00 p.m. a truck leaves
chicago for st. louis, traveling at a constant speed of 55 miles per hour. if it is a 305-mile drive between st. louis and chicago, at what time will the car and truck pass each other?
Let x = miles traveled by car Let y = miles traveled by truck.
Because the total distance is 305 miles, x + y = 305 (1)
Let t = hours of travel by truck. Because the truck speed is 55 mph, 55*t = y or t = y/55 (2)
The car has an hour head start, therefore it travels for (t + 1) hours. Because the car travels at 65 mph, 65*(t + 1) = x Substitute (2) to obtain 65*(y/55 + 1) = x or 1.1818y + 65 = x (3)
From (1), obtain 1.1818y + 65 = 305 - y 2.1818y = 240 y = 110 x = 305 - y = 195
From (2), t = 110/55 = 2 hours
The two vehicles pass each other at 2:00 pm + 2 hours = 4:00 pm
