TRANSPORTATION PROBLEMS
Here are three problems about different kinds of transportation. After
trying to solve the problems, you can check your answers to see if they are
correct. If you would like some help, click on Solutions.
1. COAL TRANSPORTATION
A power plant needs 500 tons of coal. A train is to transport the coal
using 18 full coal cars. There are 3 different types of cars, with capacities
of 15 tons, 20 tons, and 30 tons, respectively. How many of each type of coal car is there?
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2. TWO CARS AND A PLANE
The distance between Warsaw and Poznan is 300 km. A car leaves
Warsaw and travels at a constant rate of 50 km/h toward Poznan. At the same time,
a second car leaves Poznan and travels toward Warsaw also at a constant rate
of 50 km/h. Also at the same time, a plane takes off from Warsaw and flies
toward Poznan at a constant rate of 100 km/h (a rather old airplane). The
plane passes the first car and continues flying toward the second car. When
the plane meets the second car, the pilot turns around and flies back toward
the first car. When the plane reaches the first car, again the pilot turns
around and flies back toward the second car. The plane continues this
pattern until both cars meet. How many km did the plane fly?
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3. A VERY STRANGE TRAIN
A train begins with less than 100 cars. At the first station, 1/4 of all the
cars plus an additional half car are uncoupled. The train then goes on to
the second station, where 1/4 of the remaining cars, plus an additional half
car are uncoupled. The train then continues on. At the third station, 1/4 of
the remaining cars, plus an additional half car, are again uncoupled. The
train then goes on to the fourth station. How many cars arrive?
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