Question

Following a severe snowstorm, Ken and Bettina Reeves must clear their driveway and sidewalk.Ken can clear the snow by himself in 3 hours, and Bettina can clear the snow by herself in 4 hours. After Bettina has been working for 1 hour, Kane is able to join her. How much longer will it take them working together to remove the rest of the snow?

Answer 1

Using the concept of work rates of Ken and Bettina, it will take Bettina and Ken an additional 1 hour and 17 minutes to remove the rest of the snow.

Ken's work rate = 1 job / 3 hours = 1/3

Bettina's work rate = 1 job / 4 hours = 1/4

The proportion of work completed by Bettina working alone for 1 hour = 1/4

The proportion of work remaining for Bettina = 3/4 (1 - 1/4)

The combined work rate of Ken and Betetina = Ken's work rate + Bettina's work rate

Combined work rate = 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Based on the combined work rate, we can find the time it takes for them to clear the remaining 3/4 of the snow:

Time = Job / Combined work rate Time = (3/4) / (7/12) = (3/4) * (12/7) = 9/7

Thus, we can conclude that it will take Bettina and Ken an additional 9/7 hours to remove the rest of the snow when working together, which is approximately 1 hour and 17 minutes.

Answer 2

Determine how much of the job they have finished by calculating:

2/4 + 2/6 = 1/2 + 1/3 = 5/6 of the job has been done.

So, they have 1/6 of the job to go.

Then we write the following fractional equation:

t/4 + t/6 = 1/6

Multiply all by 12 (the LCD) and get

3t + 2t = 2

5t = 2

t = 2/5 hour = 24 minutes.