Delivering Grain on Time

A collective farm was due to deliver its quota of grain to the state authorities. The management of the Kolkhoz decided the trucks should arrive in the city at exactly 11:00 A.M.

If the trucks traveled at 30 miles per hour they would reach the city at ten, an hour early; at 20 miles an hour they would arrive at noon, an hour late.

How far is the Kolkhoz from the city, and how fast should the trucks travel to arrive at 11:00 A.M.?

Answer

Kolkhoz is 120 miles away from the city and the truck should travel at 24 miles an hour.

At 30 miles per hour a truck travels a mile in 2 minutes; at 20 miles per hour, in 3 minutes. At the latter speed the truck is 1 minute slower per mile. To lose 2 hours, or 120 minutes, takes 120 miles, which is how far the Kolhoz is from the city.

At 30 mph, the truck would cover 120 miles in 4 hours. The trip is to take 1 hour longer, or to arrive at 11:00 A.M., and calls for a speed of 24 (120/5) miles per hour.