Final answer:
Willie and Ndiba's combined work rate is the sum of their individual rates (1/7 + 1/8). They can together paint the fence in 56/15 or approximately 3.73 hours.
Step-by-step explanation:
When Willie and Ndiba work together to paint a fence, we need to find their combined work rate. The question is a classic example of a combined work problem in algebra.
Willie's rate of work is = 1 fence / 7 hours = 1/7 of the fence per hour.
Ndiba's rate of work = 1 fence / 8 hours = 1/8 of the fence per hour.
Their combined work rate is: (1/7 + 1/8) fences per hour.
To find out how long they would take when working together, we calculate the reciprocal of the combined work rate:
Combined work rate = 1/7 + 1/8 = 8/56 + 7/56 = 15/56
Time taken when working together = 1 / (15/56) hours = 56/15 hours
Therefore, Willie and Ndiba will take 3.73 hours (rounded to two decimal places) to complete the painting job when working together. This is a practical application of rates and time in algebra.