The cyclist rides uphill at 20 miles per hour for two hours. The total distance traveled by the cyclist is 20*2 = 40 miles. To sustain the constant speed the force exerted by the cyclist is 50 pounds. It is safe to assume that the displacement of the cyclist is in the direction of the force that is appled. 40 miles is equivalent to 5280*40 = 211200 foot. The work done by the cyclist is equal to 211200*50 = 10560000 foot-pounds.

Each foot pound is equivelent to 0.324048267 calories. The power bar provides 300 kcal and the person is able to utilize 25% of the energy. Each bar can satisfy an energy consumption of 300*0.25*1000 = 75000 calories. 10560000 foot-pound = 3421949.7 calories. The number of bars of protein he would have to eat is equal to: 3421949.7/75000 = 45.62

**The cyclist needs to eat approximately 46 power bars**