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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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Drag the tiles to list the sides of △MNO from shortest to longest.
sweet [91]

The smaller the angle subtended by a side, the smaller the length of the

side.

The correct responses are;

Question 1: The list of sides from shortest to longest are;

  • MO/Shortest MO/Medium and MO/Longest

a) <u>Friday</u>

b) <u>70 minutes</u>

c) <u>40%</u>

d) Yes<u>,</u> <u>the sum of the </u><u>mean</u><u> number of </u><u>minutes spent</u><u> on </u><u>aerobic</u><u> training and the mean number of minutes spent on </u><u>strength</u><u> training is equal to the mean </u><u>total</u><u> number of minutes spent </u><u>training.</u>

From the given diagram, we have, the measure of the third angle, ∠O, is

found as follows;

∠O = 180° - 54° - 61° = 65°

Therefore, ∠O = The largest angle

We get;

The longest side is opposite the largest angle, which gives;

The shortest side is the side opposite ∠N (54°)= \frac{}{MO}

The next shortest side is the side opposite ∠M(61°) = \frac{}{NO}

The longest side is the side opposite ∠O(65°) = \frac{}{MN}

a) The time spent training on Tuesday = 60 + 10 = 70 minutes

The time spent training on Thursday = 50 + 30 = 80 minutes

The time spent training on Friday = 45 + 40 = 85 minutes

Therefore, the day the athlete spent the longest total amount of time training is on <u>Friday</u>

b) The time spent training on Monday = 10 + 20 = 30 minutes

The time spent training on Wednesday = 20 + 15 = 35 minutes

Therefore, we get;

30, 35, 70, 80, and 85

The median total number of minutes the athlete spent training each day = <u>70 minutes</u>

<u />

c) The time spent strength training = 20 + 10 + 15 + 30 + 45 = 120

The total number of minutes the athlete spent training = 70 + 80 + 85 + 30 + 35 = 300

The  percentage spent on strength training = \frac{120}{300} × 100 = \frac{40}%

d) The mean number of minutes spent on strength training is found as follows;

Mean_{strength} =\frac{120}{5} =24

The mean number of minutes spent on aerobic training is found as follows;

Mean_{aerobic} =\frac{10+60+20+50+40}{5} =36

Mean_{strength} +Mean_{aerobic} =24+36=60

The mean total number of minutes spent training, Mean_{total} = \frac{300}{5} = 60

Therefore;

  • Mean_{strength}+Mean_{aerobic} = Mean_{total} \\

Learn more here:

brainly.com/question/2962546

4 0
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