In a race that consisted of three parts the cycling pa was 12 1/2 mile long. the running part of the race was 1/4 the distance of the cycling part. the kayaking part of the race was 1/2 the distance of the running part. what was the entire distance in miles of the race

We know that the ruining part of the race was  the distance of the cycling part. Since we know that the distance of the cycling part was  miles, we just need to multiply that distance by  to find the distance of the running part:
Distance of the running part=  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  the distance of the running part, we just need to multiply the distance of the running part by  to find the distance of the kayaking part:
Distance of the kayaking part= miles

Now that we have the distances of the three parts, lets add them to find the total distance:
Total distance= miles 

We can conclude that the total distance of the race was 17.1875 miles or expressed as a mixed fraction:  milles.