Question

Yuto and Riko went for a bike ride on the same path. When Riko left their house, Yuto was 5.25 miles along the path. If Yuto’s average speed was 0.25 miles per minute and Riko’s average speed was 0.35 miles per minute, then Riko will be behind Yuto when 0 ≤ t < 52.5, where t is time in minutes. Explain what this solution means and why t cannot be less than zero.

Answer 1

Yuto takes a lead of 5.25 miles by the time Riko leaves his house. Since we know that Riko's speed is greater than Yuto's, at some point he will be able to reach it.
If the difference in velocities is = 0.35 - 0.25 = 0.1 mile / minute, we know that the distance will be shortened by 0.1 mile / minute.

And if the speed remains constant, Riko will have reached Yuto, or will be behind him in:

5.25 miles (advantage) / 0.1 miles / minute = 52.5 minutes.
This is what the expression 0 ≤ t <52.5 refers to, because it is the time it takes Riko to reach Yuto.

And t can not be less than 0, taking into account the departure of both from home, since Riko left 21 minutes after Yuto and the time it took Riko to reach Yuto (52.5 minutes). In no case will t be less than 0.