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 per minute and Riko's average speed was 0.35 per minute, over what time period in minutes, t, starting from when Riko left the house, will Riko be Behind her brother?

The time period will be ;

10 am to 10 : 52 am

(Then she will catch up at exactly 10:52 am , 30 seconds)

Step-by-step explanation:

In this question, what we simply want to calculate is the amount of time it will take Riko to cover same distance as Yuto.

Mathematically, at any point in time;

Speed = distance/time

Let the time we are looking for be x minutes

At x minutes , Riko will be at a distance of 0.35 * x = 0.35x miles

At x minutes, Yuto will be at a distance of 5.25 miles + 0.25 * x = (5.25 + 0.25x) mikes

Kindly note that, at the time x minutes, the distance covered would have been equal;

Thus;

0.35x = 5.25 + 0.25x

0.35x -0.25x = 5.25

0.1x = 5.25

x = 5.25/0.1

x = 52.5 minutes

Over a time period of 52.5 minutes, Riko will be behind her brother ;

Since Yuto left at 10 am, the time period will be ;

10am to 10:52 am

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)