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

The solution means that Riko will be behind Yuto from the time she leaves the house, which corresponds to t = 0, until the time she catches up to Yuko after 52.5 minutes, which corresponds to t = 52.5. The reason that t cannot be less than zero is because it represents time, and time cannot be negative.

Explanation:

i just took the test <3

Answer 2

To understand the meaning of that expression, I prefer to derive it myself.

Call R the position of Riko and Y the position of Yuto.

R = 0.35*t

Y = 5.25 + 0.25*t

Riko is behind Yuto while R < Y

=> 0.35t < 5.25 + 0.25t

=> 0.35t - 0.25t < 5.25

=> 0.10t < 5.25

=> t < 5.25 / 0.10

=> t < 52.5

Given that the time starts to count since both Riko left and Yuto was 5.25 miles away, the time is always zero or positive.

Then, 0 ≤ t < 52.5 is the range of time for which Riko has not reached Yuto, and is behind him.