Many cyclists injure their knees because they don't know how to pedal properly. "The biggest mistake people make on our tours is thinking that the harder it is to pedal, the more exercise you get," says Bruce Burgess of Vermont Bicycle Touring. These people always pedal in the highest, most difficult gear they can manage.
Slow pedaling and hard pushing don't build good cycling muscles. You will develop brute strength, but no stamina. Fast pedaling in gears that feel easy develops the stuff it takes to climb hills or even mountains without getting tired.
Use bicycle gears in much the same way you use car gears. The major difference is that you don't have to shift into high to save gas, so it makes sense to pedal in the lowest instead of the highest gear you can handle. Low gears are for hill-climbing and accelerating, since you get the most power at high revolutions per minute. High gears are for high-speed travel. The correct pedaling speed is 60 to 120 revolutions of the pedal per minute on both hills and flat surfaces, and for healthy knees preferably 90-plus.
Strangely enough, most 10-speeds don't come with gear ratios low enough to make hill climbing easy. But bicycle stores can install gears that make Rock Creek Park's toughest grade a cinch.