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

15 minutes.

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:
`((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:
`((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:
`(25)/(60)\text{ hours}`

`((x)/(2))/(6)+((x)/(2))/(4)=(25)/(60)`

Using
`((a)/(b))/(c)=(a)/(bc)`, we will get:

`(x)/(2*6)+(x)/(2*4)=(25)/(60)`

`(x)/(12)+(x)/(8)=(25)/(60)`

`(2x)/(12*2)+(3x)/(8*3)=(25)/(60)`

`(2x)/(24)+(3x)/(24)=(25)/(60)`

`(2x+3x)/(24)=(25)/(60)`

`(5x)/(24)=(25)/(60)`

`(5x)/(24)*24=(5)/(12)*24`

`5x=5*2`

`(5x)/(5)=(5*2)/(5)`

`x=2`

Therefore, the distance between Kris's home and school is 2 miles.

Time = Distance/speed

`t=(2)/(8)`

`t=0.25`

`0.25* 60\text{ minutes}=15\text{ minutes}`

Therefore, it will take 15 minutes for Kris to reach home.