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: \(\frac{\frac{x}{2}}{6}\)
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: \(\frac{\frac{x}{2}}{4}\).
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: \(\frac{25}{60}\text{ hours}\)
\(\frac{\frac{x}{2}}{6}+\frac{\frac{x}{2}}{4}=\frac{25}{60}\)
Using \(\frac{\frac{a}{b}}{c}=\frac{a}{bc}\), we will get:
\(\frac{x}{2*6}+\frac{x}{2*4}=\frac{25}{60}\)
\(\frac{x}{12}+\frac{x}{8}=\frac{25}{60}\)
\(\frac{2x}{12*2}+\frac{3x}{8*3}=\frac{25}{60}\)
\(\frac{2x}{24}+\frac{3x}{24}=\frac{25}{60}\)
\(\frac{2x+3x}{24}=\frac{25}{60}\)
\(\frac{5x}{24}=\frac{25}{60}\)
\(\frac{5x}{24}*24=\frac{5}{12}*24\)
\(5x=5*2\)
\(\frac{5x}{5}=\frac{5*2}{5}\)
\(x=2\)
Therefore, the distance between Kris's home and school is 2 miles.
Time = Distance/speed
\(t=\frac{2}{8}\)
\(t=0.25\)
\(0.25\times 60\text{ minutes}=15\text{ minutes}\)
Therefore, it will take 15 minutes for Kris to reach home.
