Problem Solving

One person alone can cut the grass of a yard in 4 hours. If two people both working at that rate were to work on cutting the grass, but one person is to start and the other is to join him later, how long after the first person starts working should the second one join so that the task is completed in 3 hours?

A) Both should start at the same time
B) 45 minutes later
C) 1 hour later
D) 1 hour 20 minutes later
E) 2 hours later

OA : E

Source : Bellcurves

manik11 wrote:One person alone can cut the grass of a yard in 4 hours. If two people both working at that rate were to work on cutting the grass, but one person is to start and the other is to join him later, how long after the first person starts working should the second one join so that the task is completed in 3 hours?

A) Both should start at the same time
B) 45 minutes later
C) 1 hour later
D) 1 hour 20 minutes later
E) 2 hours later

Let the yard = 12 units.
Since each person can compete the task in 4 hours, the rate per person = w/t = 12/4 = 3 units per hour.
Thus, the combined rate for 2 people working together = 3+3 = 6 units per hour.

We can PLUG IN THE ANSWERS, which represent how long the first person works alone.
When the correct answer is plugged in, the amount of work completed in 3 hours will be 12 units.

D: 1 hour 20 minutes
At a rate of 3 units per hour, work completed by one person in 4/3 hours = rt = (3)(4/3) = 4 units.
Remaining time = 3 - 4/3 = 5/3 hours.
At a combined rate of 6 units per hour, work completed by two people in the remaining 5/3 hours = (6)(5/3) = 10 units.
Total work completed in 3 hours = 4+10 = 14 units.
Too much work is completed.
Eliminate D.

To reduce the amount of work completed, the first person must spend MORE TIME working alone.

The correct answer is E.

E: 2 hours
At a rate of 3 units per hour, work completed by one person in 2 hours = rt = (3)(2) = 6 units.
Remaining time = 3 - 2 = 1 hours.
At a combined rate of 6 units per hour, work completed by two people in the remaining 1 hour = (6)(1) = 6 units.
Total work completed in 3 hours = 6+6 = 12 units.
Success!

manik11 wrote:One person alone can cut the grass of a yard in 4 hours. If two people both working at that rate were to work on cutting the grass, but one person is to start and the other is to join him later, how long after the first person starts working should the second one join so that the task is completed in 3 hours?

A) Both should start at the same time
B) 45 minutes later
C) 1 hour later
D) 1 hour 20 minutes later
E) 2 hours later

Source : Bellcurves

If a person can cut the grass in 4 hours, that person cuts 1/4 of the lawn per hour.

So cutting the lawn takes 4 total person hours.

We want the job to get completed in 3 hours.

If one person cuts for 3 hours, he will complete 3/4 of the lawn.

So the other person needs to cut 1/4 of the lawn, meaning the second person needs to cut for 1 hour, which would be the last hour of the 3 hours.

So the second person needs to join after the first person has cut for 2 hours.

The correct answer is E.

And believe me I know of what I speak. LOL https://www.youtube.com/watch?v=Z0Y_QnL2LTM

I'd think of it this way.

Rate of one guy = 1/4 per hour
Rate of two guys together = 1/2 per hour

Suppose the first guy works for x hours alone and the two work together for y hours. Then we have

(1/4)x + (1/2)y = 1
and
x + y = 3

Multiply the first equation by 2, and we have

(1/2)x + y = 2
and
x + y = 3

So (1/2)x = 1, and x = 2, and we're done! (Note the real key here: we made x the variable for which we were solving, so we didn't have to correct too much at the end.)