We know that the ruining part of the race was [tex] \frac{1}{4} [/tex] the distance of the cycling part. Since we know that the distance of the cycling part was [tex]12 \frac{1}{2} [/tex] miles, we just need to multiply that distance by [tex] \frac{1}{4} [/tex] to find the distance of the running part:
Distance of the running part= [tex] 12 \frac{1}{2} * \frac{1}{4} = 12.5*0.25=3.125 [/tex] miles
Now that we have the distance of the cycling part, we can find the distance of the kayaking part.
Since we know that the distance of the kayaking part was [tex] \frac{1}{2} [/tex] the distance of the running part, we just need to multiply the distance of the running part by [tex] \frac{1}{2} [/tex] to find the distance of the kayaking part:
Distance of the kayaking part=[tex]3.125* \frac{1}{2} =3.125*0.5=1.5625[/tex] miles
Now that we have the distances of the three parts, lets add them to find the total distance:
Total distance=[tex]12.5+3.125+1.5625=17.1875[/tex] miles
We can conclude that the total distance of the race was 17.1875 miles or expressed as a mixed fraction: [tex]17 \frac{3}{16} [/tex] milles.
