To achieve the maximum benefit for the heart when exercising, your heart rate (in beats per minute) should be in the target heart rate zone. The lower limit of this zone is found by taking 70% of the difference between 220 and your age. The upper limit is found by using 85%. Source: Physical Fitness.

a. Find formulas for the upper and lower limits (u and l) as linear equations involving the age x.
b. What is the target heart rate zone for a 20-year-old?
c. What is the target heart rate zone for a 40-year-old?
d. Two women in an aerobics class stop to take their pulse and are surprised to find that they have the same pulse. One woman is 36 years older than the other and is working at the upper limit of her target heart rate zone. The younger woman is working at the lower limit of her target heart rate zone. What are the ages of the two women, and what is their pulse?
e. Run for 10 minutes, take your pulse, and see if it is in your target heart rate zone.