Question

The coach requires his players to practice six and one over two.hours each week. The table below shows how long Jackson practiced this week. How much time does he need to practice in his last practice session meet his coach’s requirement?

Practice Session
Time (hours)
1
time in hours. one and one over six.
2
time in hours. two and one over two.
3
time in hours. two over three
4
?










two and one over three hours

two and one over six hours

two and five over six hours

four and one over three

Answer 1

`2(1)/(6)\ hours`

Explanation:

Given

`Session\ 1: 1(1)/(6)`

`Session\ 2: 2(1)/(2)`

`Session\ 3: (2)/(3)`

`Total\ Time = 6(1)/(2)`

Required

Determine the time in the last session

Represent the 4th session with x

So, we have:

`Session\ 1 + Session\ 2 + Session\ 3 + x = Total\ Time`

Substitute values for Session 1-3 and Total Time

`1(1)/(6) + 2(1)/(2) + (2)/(3) + x = 6(1)/(2)`

Collect Like Terms

`x = 6(1)/(2) - 1(1)/(6) - 2(1)/(2) - (2)/(3)`

Convert to improper fractions

`x = (13)/(2) - (7)/(6) - (5)/(2) - (2)/(3)`

Take LCM

`x = (39 - 7 - 15 - 4)/(6)`

`x = (13)/(6)`

Convert to improper fraction

`x = 2(1)/(6)`

Hence, the time left is
`2(1)/(6)\ hours`