Question

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?

Answer 1

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