Hi my friend plays this game called Animal jam classic, all she's wanted was a membership, but her fam can't afford it, both of
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Convert 36 4/9 to an improper fraction. Use this rule: a b/c = ac + b/c
-36 × 9 + 4/9 - (-10 2/9) - 18 2/9
Simplify 36 × 9 to 324
- 324 + 4/9 - (-10 2/9) - 18 2/9
Simplify 324 + 4 to 328
- 328/9 - (-10 2/9) - 18 2/9
Convert 10 2/9 to an improper fraction. Use this rule: a b/c = ac + b/c.
-328/9 - (- 10 × 9 + 2/9) - 18 2/9
Simplify 10 × 9 to 90
-328/9 - (- 90 + 2/9) - 18 2/9
Simplify 90 + 2 to 92
- 328/9 - (-92/9) - 18 2/9
Convert 18 2/9 to an improper fraction. Use this rule: a b/c = ac + b/c.
-328/9 - (- 92/9) - 18 × 9 + 2/9
Simplify 18 × 9 to 162
-328/9 - (- 92/2) - 162 + 2/9
Simplify 162 + 2 to 164
-328/9 - (- 92/9) - 164/9
Simplify brackets
-328/9 + 92/9 - 164/9
Join the denominators
-328 + 92 - 164/9
Simplify
-400/9
Convert to a mixed fraction
It takes 9 hrs 19.8 minutes for the student teacher to grade the exams if they worked alone
<u>Solution:</u>
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
---- 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
Equating eqn 1 and 2
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, <em>total time taken by the student teacher = total work ÷ efficiency of student teacher</em>
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