Question

11. A three-person relay race consists of ten times around a football field. If Tomiko runs three and one-sixth times and Brianna runs two and two-thirds times around the field, how many times around the field does the third person have to run to finish the race?

Answer 1

If Tomiko runs three and one-sixth times and Brianna runs two and two-thirds times around the field

Tomiko runs three and one-sixth times =
`3(1)/(6) =(19)/(6)`

Brianna runs two and two-thirds times =
`2(2)/(3) =(8)/(3)`

relay race consists of ten times around a football field

Tomiko + Brianna + third person = 10

Let the third person is x

`(19)/(6) + (8)/(3) +x = 10`

Take common denominator LCD, that is 6

Multiply the whole equation by 6

19 + 16 + 6x = 60

35 +6x = 60

6x = 25

`x=(25)/(6) = 4(1)/(6)`

The third person have to run
`4(1)/(6)` times to finish the race