Question

Working together, Lisa and Wilbur can dig a 10 ft by 10 ft hole in 3.33 hours. If Wilbur had done it alone, it would have taken him 10 hours. Find how long it would take Lisa to do it alone.

A) 4.99
B) 6.07
C) 5.9
D) 5.81

Answer 1

Lisa would take approximately 4.98 hours to dig the hole on her own, which is closest to option A) 4.99. This is determined by finding the combined work rate, subtracting Wilbur's work rate, then taking the reciprocal of Lisa's work rate.

Step-by-step explanation:

The question given is a work rate problem that can be solved using the concept of individual work rates adding up to a combined work rate. To solve this problem, we should first determine the rate at which Lisa and Wilbur, when working together, dig the hole.

Lisa and Wilbur together dig the hole in 3.33 hours, so their combined work rate is the reciprocal of this time, which is 1/3.33 (holes per hour). Wilbur alone would take 10 hours, making his work rate 1/10. To find Lisa's work rate, we subtract Wilbur's work rate from their combined work rate:

Lisa's work rate = (1 / 3.33) - (1 / 10)

When calculating this, we find that Lisa's work rate is approximately 0.201 holes per hour. To find the time it would take for Lisa to dig the hole on her own, we take the reciprocal of her work rate:

Time = 1 / 0.201

Therefore, it would take Lisa approximately 4.975 hours to dig the hole alone, which, when rounded to two decimal places, is 4.98 hours. This is closest to option A) 4.99.