Work/Rate Problem

[franciskyle]

Question:

If 4 men working at the same rate can do 2/3 of a job in 40 minutes, how many minutes would it take 1 man working at this rate to do 2/5 of the job?

Answers:

80, 88, 92, 96, 112

How would you tackle this problem?

Below is how I solved it, but I feel like there is an easier way to do this problem. Any suggestions? How would you rate this problems difficulty?

WARNING: SPOILER BELOW:





2/3 Job / 4 Men = (2/3)/4 = 1/6... therefore each man does 1/6 of the job in 40 minutes.

1/6 Job / 40 minutes = (1/6)/40 = 1/240... therefore each man does 1/240 of the job per minute

Using Distance (Work) = Rate * Time

2/5 = 1/240 * time

2/5 * 240 = time

48 * 2 = 96

[scoobydooby]

another approach by unitary method

no of men is inversely proportional to the time taken

if 4 men do 2/3 W in 40 mins
1 man does 2/3 W in 40*4=160 mins

1 man 2/3W in 160 mins
1 man 2/5W in 160*3/2*2/5=96 mins

[dtweah]

Question:

If 4 men working at the same rate can do 2/3 of a job in 40 minutes, how many minutes would it take 1 man working at this rate to do 2/5 of the job?

Answers:

80, 88, 92, 96, 112

How would you tackle this problem?

Below is how I solved it, but I feel like there is an easier way to do this problem. Any suggestions? How would you rate this problems difficulty?

WARNING: SPOILER BELOW:





2/3 Job / 4 Men = (2/3)/4 = 1/6... therefore each man does 1/6 of the job in 40 minutes.

1/6 Job / 40 minutes = (1/6)/40 = 1/240... therefore each man does 1/240 of the job per minute

Using Distance (Work) = Rate * Time

2/5 = 1/240 * time

2/5 * 240 = time

48 * 2 = 96

(4 man x 40 min )160 man-minute = 2/3X, where X is number of man-minutes originally required. X=240 man-minutes. 2/5 of 240 man minutes. 96man min. 1 man x 96 mins = 96 man mins. Leave all that 1/6 job analysis begin (laugh).