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Aleksandr-060686 [28]
3 years ago
5

Tyrell exercised this week both by walking and by biking. He walked at a rate of 4 mi/h and biked at a rate of 12 mi/h. The tota

l distance he covered both walking and biking was 36 miles and Tyrell spent one more hour walking than biking.
A. Define a variable and write an equation for this solution.

B. How many hours did Tyrell spend on each activity?
Mathematics
1 answer:
Flura [38]3 years ago
5 0

Answer:

A. The equation is 4(t + 1) + 12t = 36

B. He spent 2 hours on biking and 3 hours on walking

Step-by-step explanation:

* Lets explain how to solve the problem

- Tyrell walked at a rate 4 miles per hour

∴ His speed on walking is 4 miles/hour

- Tyrell biked at rate 12 miles per hour

∴ His speed on biking is 12 miles/hour

- The total distance he covered both walking and biking was

  36 miles

- Assume that he walked x and biked y

∴ x + y = 36 ⇒ (1)

- Tyrell spent one more hour walking than biking

- Assume that he biked for t hours

∵ He walked one more hour than he biked

∵ He biked for t hours

∴ He walked for t + 1 hours

A.

∵ Distance = speed × time

∴ x = 4 × (t + 1)

∴ x = 4(t + 1)

∴ y = 12 × t

∴ y = 12t

- Substitute x and y in equation (1)

∴ 4(t + 1) + 12t = 36 ⇒ the equation

B.

* Lets solve the equation

- Multiply the bracket by 4

∴ 4t + 4 + 12t = 36

- Add like terms in left hand side

∴ (4t + 12t) + 4 = 36

∴ 16t + 4 = 36

- Subtract 4 from both sides

∴ 16t = 32

- Divide both sides by 16

∴ t = 2

∵ t represents the time of biking

∴ He biked for 2 hours

∵ t + 1 represents the time of walking

∵ t + 1 = 2 + 1  = 3

∴ He walked for 3 hours

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The mean resting pulse rate for men is 72 beats per minute. A simple random sample of men who regularly work out at Mitch's Gym
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Answer:

We conclude that the mean resting pulse rate for men is 72 beats per minute.

Step-by-step explanation:

We are given that he mean resting pulse rate for men is 72 beats per minute. Assume that the standard deviation of the resting pulse rates of all men who work out at Mitch's Gym is known to be 2.6 beats per minute.

A simple random sample of men who regularly work out at Mitch's Gym is obtained and their resting pulse rates (in beats per minute) are listed below;

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SO, Null Hypothesis, H_0 : \mu = 72 beats/minute     {means that the mean resting pulse rate for men is 72 beats per minute}

Alternate Hypothesis, H_A : \mu < 72 beats/minute      {means that the mean resting pulse rate for men is less than 72 beats per minute}

The test statistics that would be used here <u>One-sample z-test statistics</u> as we know about population standard deviation;

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<u></u>

<u>Also, P-value of the test statistics is given by;</u>

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3 years ago
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