APPROACH #1: Assign a convenient value to the bicyclist's original speed
Let's say the original speed is 100 kilometers per hour.
When we increase 100 by 30%, we get: 100 + (30% of 100) = 100 + 30 = 130
When we increase 130 by 10%, we get: 130 + (10% of 130) = 130 + 13 = 143
So, the speed increased from 100 kilometers per hour to 143 kilometers per hour.
The percent increase = 100(new - old)/old = 100(143 - 100)/100 = 43%
Answer: C

APPROACH #2: Assign a variable to the bicyclist's original speed
Let x = the original speed in kilometers per hour.
When we increase x by 30%, we get: x + (30% of x) = x + 0.3x = 1.3x
When we increase 1.3x by 10%, we get: 1.3x + (10% of 1.3x) = 1.3x + 0.13x = 1.43x
So, the speed increased from x kilometers per hour to 1.43x kilometers per hour.
The percent increase = 100(new - old)/old = 100(1.43x - x)/x = 43%
Answer: C