Answer:
15 minutes.
Step-by-step explanation:
Let x represent the distance from home to school.
Kris runs half of the distance to school averaging 6 mph.
Time = Distance/speed
Time taken to cover the half distance (x/2) at a rate of 6 mph would be: [tex]\frac{\frac{x}{2}}{6}[/tex]
He jogs the rest of the way to school averaging 4 mph. Time taken to cover the half distance (x/2) at a rate of 4 mph would be: [tex]\frac{\frac{x}{2}}{4}[/tex].
Time taken to complete the distance (x) is 25 minutes.
Speed is miles pr hour, so we need to convert time from minutes to hours as: [tex]\frac{25}{60}\text{ hours}[/tex]
[tex]\frac{\frac{x}{2}}{6}+\frac{\frac{x}{2}}{4}=\frac{25}{60}[/tex]
Using [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex], we will get:
[tex]\frac{x}{2*6}+\frac{x}{2*4}=\frac{25}{60}[/tex]
[tex]\frac{x}{12}+\frac{x}{8}=\frac{25}{60}[/tex]
[tex]\frac{2x}{12*2}+\frac{3x}{8*3}=\frac{25}{60}[/tex]
[tex]\frac{2x}{24}+\frac{3x}{24}=\frac{25}{60}[/tex]
[tex]\frac{2x+3x}{24}=\frac{25}{60}[/tex]
[tex]\frac{5x}{24}=\frac{25}{60}[/tex]
[tex]\frac{5x}{24}*24=\frac{5}{12}*24[/tex]
[tex]5x=5*2[/tex]
[tex]\frac{5x}{5}=\frac{5*2}{5}[/tex]
[tex]x=2[/tex]
Therefore, the distance between Kris's home and school is 2 miles.
Time = Distance/speed
[tex]t=\frac{2}{8}[/tex]
[tex]t=0.25[/tex]
[tex]0.25\times 60\text{ minutes}=15\text{ minutes}[/tex]
Therefore, it will take 15 minutes for Kris to reach home.
