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ryzh [129]
3 years ago
11

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 tr

ip 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?
Mathematics
2 answers:
vodomira [7]3 years ago
5 0
Find the space,

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

Divide by velocity,

t=2/8=0.25\ \ hours=15\ \ minutes
lozanna [386]3 years ago
5 0

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.

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