A farmer can plow a field in 4days using a tractor.A hired hand can plow the same field in 400days using a hoe

Question

a. How many days will be required for plowing if a tractor and 10 hired hands will work together?

b. A tractor and 10 hired hands working together are expected to finish the job at a certain time as answered in the first problem. If the tractor and 10 hired hands worked together at first and then on the end of the second day, the tractor broke down, how many more workers are needed to be hired to finish the job on time?

Please answer with explanation. Thanks!

Answer 1

a. tractor: (1/4)Days = fraction of job done ) and D=4 and the job is done
Likewise for a hired hand (1/400)D = fraction of job done
If there are N hands then the rate is N/400

There is one tractor and 10 hands so
(1/4 + 10/400) D = 1 (the whole job)
(1/4 + 1/40) D = (44/160)D = 1

So Number of days = 160/44 = 3.6363636363

b. In one day, one tractor and 10 men will do:
(1/4 + 1/40)1 = fraction job done = 0.275
This means that 0.725 of the job reamains to be done.

Since the tractor is down, you will need N additional hands so:
(1/40 + N/400)(Time Remaining) = 0.725
time remaining = 3.63636363 - 1 = 2.63636363

(1/40 + N/400) = 0.725/2.63636363
N/400 = 0.275 - 1/40 = 0.25
N = 100 extra hands are needed to finish the job in time

An easier way is to say that the tractor is the equivalent of 100 hand since it can do the job in 4 days and it takes 1 hand 400 days or 100 hands 4 days.

Answer 2

The tractor can plow 1/4 of a field per day and each hired hand can plow 1/400 field in a day. The tractor can therefore plow as fast as 100 hands. The ten hands and the tractor can plow 11/40 of the field in one day, so it will take 40/11 (3-4/11 days, if you prefer mixed numbers) to plow the field.

Not allowing for the time necessary to buy the hoes and process the 100 hands necessary to pinch-hit for the disabled tractor, it will take than many extra hands to get the job done in the same amount of time.

Whoever dreamed up this problem clearly isn't a farmer!

Answer 3

Let
x = time for tractor and 10 hired hands working together

4 = time tractor
40 = time 10 hired hands

x/4 + x/40 = 1
10x + x = 40
11x = 40
x = 40/11 days = 3 7/11 days

Answer 4

A tractor takes 4 days. 10 guys are 1/40th as fast. That is 4/40 or 1/10 subtracted from the time. It would be close to 3.9 days.

I am a bit rusty at math problems though.