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Answer :
Big D swam 8 miles, ran 56 miles, and biked 168 miles, based on solving a system of equations derived from the relationship between the distances covered in each triathlon activity.
To determine how many miles Big D trained for each activity during the week, we can set up a system of equations based on the information given. Let's denote the number of miles he swam as s, the number of miles he ran as r, and the number of miles he biked as b. According to the problem, he ran seven times as much as he swam and biked three times as far as he ran. Also, the total distance for all three activities is given as 232 miles.
From the problem we can establish the following equations:
r = 7s
b = 3r
s + r + b = 232
By substituting r and b in the third equation with their equivalents in terms of s from the first and second equations, we get:
s + 7s + 3(7s) = 232
s + 7s + 21s = 232
29s = 232
Now, dividing both sides by 29 to solve for s:
s = 232 / 29
s = 8 miles
Then, we plug in s into the first equation to find r:
r = 7 × 8
r = 56 miles
Finally, we use the value of r to find b:
b = 3 × 56
b = 168 miles
Therefore, Big D swam 8 miles, ran 56 miles, and biked 168 miles over the course of that week.
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