Question

A high school mathematics teacher can grade a set of exams in 7 hours working alone. If their student teacher helps​ them, it will take them 4 hours to grade the exams together. How long would it take the student teacher to grade the exams if they worked​ alone?

Answer 1

It takes 9 hrs 19.8 minutes  for the student teacher to grade the exams if they worked​ alone

Solution:

Let the efficiency of the school teacher be “x” and the efficiency of the student teacher be “y”

Here the word efficiency means the rate of doing work

Let the total work to be completed be W

According to the question,

The time taken by the school teacher to complete the work is 7 hrs.

So we can write it in equation form

$W = x \times 7$  ---- eqn 1

where W is the total work and x is the efficiency

Similarly for student teacher and school teacher doing the work simultaneously, we can write the equation as

$W =(x +y ) \times 4$

Equating eqn 1 and 2

$x \times 7=(x+y) \times 4$

7x = 4x + 4y

3x = 4y

So in ratio x : y = 4 : 3

Now putting value of x = 4 in equation (1) we get total work to be 28

Now, total time taken by the student teacher = total work ÷ efficiency of student teacher

Hence, total time taken by the student teacher = 28 ÷ 3 = 9.33 hrs

= 9 hrs 19.8 minutes

Hence it takes 9 hrs 19.8 minutes  for the student teacher to grade the exams if they worked​ alone