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Mixing Water and Antifreeze The cooling system of a certain foreign-made car has a capacity of 15 liters. If the system is filled with a mixture that is \(40 \%\) antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is \(60 \%\) antifreeze?

How much water must be evaporated from 32 ounces of a \(4 \%\) salt solution to make a \(6 \%\) salt solution?

The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold. Thus, 18-karat gold is \(\frac{18}{24},\) or \(75 \%\) pure gold; 12 -karat gold is \(\frac{12}{24},\) or \(50 \%\) pure gold; and so on. How much 12-karat gold should be mixed with pure gold to obtain 60 grams of 16-karat gold?

Molecules A sugar molecule has twice as many atoms of hydrogen as it does oxygen and one more atom of carbon than of oxygen. If a sugar molecule has a total of 45 atoms, how many are oxygen? How many are hydrogen?

Solve each equation, if possible. $$ \frac{3}{x}-\frac{1}{3}=\frac{1}{6} $$

An air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of \(30 \mathrm{mi} / \mathrm{h}\), how far can it fly and return safely? (Assume that the wind remains constant.)

An oil tanker can be emptied by the main pump in 4 hours. An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at 9 AM, when should the auxiliary pump be started so that the tanker is emptied by noon?

Filling a Tub A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?

A Biathlon Suppose that you have entered an 87 -mile biathlon that consists of a run and a bicycle race. During your run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?

In the 2016 Olympics, Usain Bolt of Jamaica won the gold medal in the 100 -meter race with a time of 9.81 seconds. In the 1896 Olympics, Thomas Burke of the United States won the gold medal in the 100-meter race in 12.0 seconds. If they ran in the same race, repeating their respective times, by how many meters would Bolt beat Burke?