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?

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 =

Brianna runs two and two-thirds times =

relay race consists of ten times around a football field

Tomiko  + Brianna + third person = 10

Let the third person is x

Take common denominator LCD, that is 6

Multiply the whole equation by 6

19 + 16 + 6x = 60

35 +6x = 60

6x = 25

The third person have to run times to finish the race

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)