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

Answer: 4:00 pm