Word Problem involving work

If a farmer can plough a field with a tractor in 4 hours, what fraction of the field is ploughed in 1 hour? If the farmer uses his new tractor the same field could be done in 3 hours. How long would it take to plough the field if he uses both tractors?

If a farmer can plough a field with a tractor in 4 hours, what fraction of the field is ploughed in 1 hour? 1/4 of the field

If the farmer uses his new tractor the same field could be done in 3 hours. How long would it take to plough the field if he uses both tractors?

He is plowing at a rate of 1/4 + 1/3 = 7/12 fields per hour

so the time plow 1 field is (1 field) / (7/12 fields per hour) = 12/7 hours = 1.7143 hours

Since 1 field can be plowed every 4 hours, we see that 1/4 of the field can be plowed per hour.

Then, the new tractor can plow 1/3 of the field per hour. If both trackers work together, they can plow 1/4 + 1/3 = 7/12 of the field per hour. Thus, it would take him 1/(7/12) = 12/7 hours to plow the field.

I hope this helps!

If a farmer can plough a field with a tractor in 4 hours, what fraction of the field is ploughed in 1 hour? 1/4
of the field.
If the farmer uses his new tractor the same field could be done in 3 hours. How long would it take to plough the field if he uses both tractors? 7/2=3.5 hours

The first equation is obvious. The farmer will have completed plowing 1/4 of the field in 1 hour.

For the next question:

Let x be the time that it takes the farmer to plow both fields:

1/3 + 1/4 = 1/x

x = 12/7 hours

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