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Savatey [412]
3 years ago
5

Solve the following word problem. A man travels from Town X to Town Y at an average rate of 50 mph and returns at an average rat

e of 40 mph. He takes a 1/2 hour longer than he would take if he made the round trip at an average of 45 mph. What is the distance from Town X to Town Y?
Mathematics
1 answer:
777dan777 [17]3 years ago
7 0
Distance = rate*time

Let distance from X to Y be 'd' 

From the equation we can solve for 'time'

time = distance/rate

The total time it takes to go 50 mph ,then 40 mph is:

\frac{d}{50} + \frac{d}{40}

The total time it takes to go 45 mph round trip is:

\frac{2d}{45}

We know that the round-trip at 45 mph takes half-hour shorter, so by adding '1/2' to its time it will be equal to the time to go 50 then 40.

\frac{2d}{45} + \frac{1}{2} = \frac{d}{50} + \frac{d}{40} \\  \\ \frac{4d+45}{90} = \frac{9d}{200} \\  \\ 800d+9000 = 810d \\  \\ 10d = 9000 \\  \\ d = 900

Answer: The distance from X to Y is 900 miles.

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3 years ago
Zahra compares two wireless data plans. Which equation gives the correct value of n, the number of GB, for which Plans A and B c
Elden [556K]

The equation which gives the correct value of n, the number of GB, for which Plans A and B cost the same is 8n = 20 + 6(n-2)

To determine which equation gives the correct value of n, the number of GB, for which Plans A and B cost the same, we will first solve the equations.

  • For the first equation

8n = 20 + 6n

Collect like terms

8n - 6n = 20

2n = 20

Then, n = 20 ÷ 2

n = 10 GB

For Plan A

No initial fee and $8 for each GB

Here, 10GB will cost 10 × $8 = $80

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 10GB will cost $20 + (8 × $6) = $20 + $48 = $68

∴ Plans A and B do not cost the same here.

  • For the second equation

8n = 20(2n) + 6

First, clear the bracket

8n = 40n + 6

Now, collect like terms

40n - 8n = 6

42n = 6

∴ n = 6 ÷ 42

n = 1/7 GB

For Plan A

No initial fee and $8 for each GB

Here, 1/7GB will cost 1/7 × $8 = $1.14

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 1/7GB will cost $20 (Since the lowest cost is $20)

∴ Plans A and B do not cost the same here.

  • For the third equation

8n = 20 + 6(n-2)

First, clear the brackets

8n = 20 + 6n - 12

Now, collect like terms

8n - 6n = 20 - 12

2n = 8

n = 8 ÷ 2

n = 4 GB

For Plan A

No initial fee and $8 for each GB

Here, 4GB will cost 4× $8 = $32

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 4GB will cost $20 + (2 × $6) = $20 + $12 = $32

Plans A and B do not cost the same here.

∴ Plans A and B do cost the same here

  • For the fourth equation

8n = 20 + 2n + 6

Collect like terms

8n - 2n = 20 + 6

6n = 26

n = \frac{26}{6}

n = \frac{13}{3} GB or 4\frac{1}{3} GB

For Plan A

No initial fee and $8 for each GB

Here, \frac{13}{3} GB will cost \frac{13}{3}  × $8 = $34.67

For Plan B

$20 for the first 2GB and $6 for each additional GB after the first 2

Here, 4\frac{1}{3}GB will cost $20 + ( 2\frac{1}{3}× $6) = $20 + $14 = $34

∴ Plans A and B do not cost the same here.

Hence, the equation which gives the correct value of n, the number of GB, for which Plans A and B cost the same is 8n = 20 + 6(n-2)

Learn more here: brainly.com/question/9371507

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Given expressions:

  Area of a rectangle  = L W

  Area of a triangle = \frac{1}{2} B H

Problem;

Create problems using the formula;

Solution:

Problem 1; Find the area of a rectangle whose length is 10cm and the width is half the size of the length?

    Given parameters:

    Length of rectangle  = 10cm

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So, the area of the rectangle = 10cm x 5cm  = 50cm²

2. A triangle with a base length of 30cm and a height of 2cm will have an area of what?

    Given parameters:

         base length  = 30cm

         height  = 2cm

 Solution:

   Area of a triangle  = \frac{1}{2} x b x h

   Area of a triangle  = \frac{1}{2} x 30 x 2  = 30cm²

The area of the triangle will be 30cm²

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3 years ago
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