Question

Kris runs half of the distance to school averaging 6mph. He jogs the rest of the way to school averaging 4 mph, and the whole trip takes him 25 minutes. How many minutes will it take him to run the same way home if he averages 8 mph the whole way?

Answer 1

Find the space,

$x/12+x/8=25/60\Rightarrow x=2\ \ miles$

Divide by velocity,

$t=2/8=0.25\ \ hours=15\ \ minutes$

Answer 2

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.