Juanita wants participate in 20 km bicycle race. She is considering using 1 of the 2 training programs below: Program A: Ride 10 km on the first day and increase the distance by an additional 500 m each day Program B: Ride 7,500 m on the first day and increase the distance by an additional 0.75 km each day. If Juanita chooses Program A, on which day she ride on the first 15 km for the first time

Question

Juanita wants participate in 20 km bicycle race. She is considering using 1 of the 2 training programs below:   Program A: Ride 10 km on the first day and increase the distance by an additional 500 m each day Program B: Ride 7,500 m on the first day and increase the distance by an additional 0.75 km each day. If Juanita chooses Program A, on which day  she ride on the first 15 km for the first time

anonymous · Answer

It's an arithmetic progression with first term 10km and common difference 0.5km. We need to increase by 5km and 5km/0.5km = 10 so we need to increase the distance 10 times. So it is on eleventh day.

Alternatively you can do it more algebraically, saying, $$x = a + (n-1)d \implies 15 = 10 + \frac{1}{2}(n-1)$$ and solve it.