Question

Yuto left his house at 10 a. m. to go for a bike ride. By the time Yuto’s sister Riko left their house, Yuto was already 5.25 miles along the path they both took. If Yuto’s average speed was 0.25 miles per minute and Riko’s average speed was 0.35 miles per minute, over what time period in minutes, t, starting from when Riko left the house, will Riko be behind her brother? Riko will be behind Yuto when 0 ≤ t < minutes.

Answer 1

-- When Riko left the house, Yuto was 5.25 miles ahead of her.  

-- From the time she left the house, she gained (0.35 - 0.25) = 0.1 mile on Yuto 
every minute ... closing the gap at the rate of 0.1 mile per minute.

-- If she can keep it up, she'll close the gap in (5.25 / 0.1) = 52.5 minutes.

-- Riko is behind her brother when  0 ≤ t < 52.5 minutes .

Answer 2

 Riko left the house and Yuto was 5.25 miles ahead of her.  
From the time when she left the house, she gained 0.35 - 0.25 = 0.1 mile on Yuto for every minute at the rate of 0.1 mile per minute.
 If Riko can keep it up, she'll catch up to Yuto in 52.5 mins.
 5.25 / 0.1 = 52.5 minutes.
 Riko is behind her brother when 0 $\leq$ t < 52.5 minutes.