Question

Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance by the same amount each week of training. During week 6, Jacob runs 14 miles per day, which is 1.5 miles more per day than he ran during week 5. Which equation represents the daily running distance, in miles, as a function of time, t, in weeks?
a.f(t) = 0.5t + 7
b.f(t) = 0.5t + 11
c.f(t) = 1.5t + 5
d.f(t) = 1.5t + 12.5

Answer 1

Given:
Week 6 = 14 miles
Week 5 = 1.5 miles less than week 6.

1.5 miles is the common difference.

Week 6 = 14 miles
Week 5 = 12.5 miles
Week 4 = 11 miles
Week 3 = 9.5 miles
Week 2 = 8 miles
Week 1 = 6.5 miles

f(t) = first term + common difference(t-1)
f(t) = 6.5 miles + 1.5 miles (t-1)

f(1) = 6.5 + 1.5(1-1)
f(1) = 6.5 miles

f(2) = 6.5 + 1.5(2-1)
f(2) = 6.5 + 1.5
f(2) = 8 miles