Question

A father and his son are both farmers. The father has a very old tractor and the son a powerfull brand new one. If the father plow with his old tractor the corn fields he need 3 days, If the son does the same with his new tractor, he needs half the time compared to his father. How much time they need if they work together for plowing the corn fields, if they do not interfere with each other ?​

Answer 1

Answer:

9 hours ,if they work together

Answer 2

Given :- The father plow with his old tractor the corn fields he need 3 days, If the son does the same with his new tractor, he needs half the time compared to his father.

To Find :- How much time they need if they work together for plowing the corn fields, if they do not interfere with each other ?

Solution :-

Basic Method :-

→ In 3 days father plow the corn field = 1

So,

→ In 1 day father plow the corn field = (1/3)

now,

→ Time taken by son to plow the corn field = Half the time taken by father = (3/2) days .

So,

→ In (3/2) days son plow the corn field = 1

→ In 1 day son plow the corn field = (2/3)

then,

→ In 1 day both father and son plow the corn field = (1/3) + (2/3) = (3/3) = 1 .

therefore, they need only 1 day if they work together for plowing the corn fields .

LCM Method :-

→ Time taken by father to plow the corn field = 3 days

→ Time taken by father to plow the corn field = (3/2) days .

So,

→ LCM of 3 and (3/2) = 3 units = Let total work done .

then,

→ Efficiency of father = Total work / Time taken = 3/3 = 1 unit / day

→ Efficiency of son = Total work / Time taken = 3/(3/2) = 3 * (2/3) = 2 unit / day

therefore,

→ Efficiency of father and son together = 1 + 2 = 3 units / day .

hence,

→ Time taken by them to complete the work together = Total work / Total efficiency = 3/3 = 1 day (Ans.)

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