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Crank
3 years ago
11

If Dr. Bob ride his bike to his office he averages 12 mph if he drives his car he averages 48 mph his time driving is 1/4 hour l

ess than his time bicycling how far is his office
Mathematics
1 answer:
Mazyrski [523]3 years ago
7 0

Answer:

2.4 miles

Step-by-step explanation:

From the question;

  • When using the bike, speed is 12 mph
  • When using the car, the speed is 48 mph
  • He takes 1/4 hrs less when using the car than when he uses the bike.

We are going to assume the distance to the office is x miles

Therefore;

Time taken when using the bike;

Time = distance ÷ speed

         = x/12 hours

Time taken when using the car;

Time = x/48 hours

But, time taken when using the car is 1/4 hours less.

Therefore;

1/12 hours - x/48 hours = 1/4 hr

That is;

\frac{x}{12} + \frac{x}{48}= \frac{1}{4}

We want to solve for x.

Multiplying by LCM, 48

We get, 4x + x = 12

  5x = 12

    x = 12/5

      = 2.4 miles

Therefore, the office is 2.4 miles away.

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Over [174]

a. \boxed{y-602=\frac{2}{3}(x-3)}

b. For every month the pine tree grows about 0.67 inches.

c. <em> </em>It represents the height of the tree at the moment Ariel started to record the heights.

<h2>Explanation:</h2>

<h3>PART A.</h3>

In this exercise we have that in July Ariel recorded the height of a pine tree and how quickly it was expected to grow in next several months. From the Table, we can get the following points:

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It is obvious that this problem follows a linear equation, so our goal is to find the equation that matches the Table.

The point slope form of the equation of a line is:

y-y_{1}=m(x-x_{1}) \\ \\ Where: \\ \\ m:Slope \\ \\ (x_{1}, y_{1}):A \ point \ on \ the \ line

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(x_{1}, y_{1}) \rightarrow (3,602) \\ \\ \boxed{y-602=\frac{2}{3}(x-3)}

<h3>PART B.</h3>

In this case, we have that:

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  • The y-axis represents the <em>Height  of the Tree </em>in inches.

Since the slope o a line is:

Slope=\frac{Change \ in \ y}{Change \ in \ x}=\frac{2}{3}

Then, this means that<em> every three months the pine tree grows two inches, </em><em>or </em><em>for every month the pine tree grows about 0.67 inches.</em>

<h3>PART C.</h3>

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So the y-intercept is y=600 and<em> represents the height of the tree at the moment Ariel started to record the heights.</em>

<h2>Learn more:</h2>

Slope Intercept form: brainly.com/question/4192440

#LearnWithBrainly

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