1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Rasek [7]
3 years ago
7

Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train

is 3mph greater than the speed of the eastbound train. After 3 hours, they are 468 miles apart. Find the rate of each train. Assume that the trains travel in a straight line in directly opposite directions
Mathematics
1 answer:
Viefleur [7K]3 years ago
4 0

Answer:

<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>

Step-by-step explanation:

1. Let's review all the information provided for solving this question:

Eastbound train speed = x

Westbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)

Duration of trip = 3 hours

Distance between trains after 3 hours = 468 miles

2. Let's find the speed of each train, using the following equation:

3x + 3(x + 3) = 468

3x + 3x + 9 = 468

6x + 9 = 468

6x = 468 - 9 (Subtracting 9 at both sides)

6x = 459

x = 459/6 (Dividing by 6 at both sides)

x = 76.5 miles per hour

<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>

3. Proof that x = 76.5 is correct

3x + 3(x + 3) = 468

3 (76.5) + 3 (76.5 + 3) = 468

229.5 + 238.5 = 468

<u>468 = 468</u>

<u>The value of x = 76. 5 is correct. And now we know that the  Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.</u>

You might be interested in
Is 7/10 less than 2/4?
lilavasa [31]

Answer:

No

Step-by-step explanation:

7/10 is 0.7

2/4 is 0.5

0.7>05

5 0
3 years ago
Read 2 more answers
Julie and mark are selling wrapping paper for a school fundraiser. Julie sold 13 rolls of plain wrapping paper and 8 rolls of ho
patriot [66]

Answer:

Cost of one roll of plain wrapping paper is $12 and Cost of one roll of holiday paper is $17.

Step-by-step explanation:

Solution,

Let the cost of 1 plain wrapping paper be x.

And the cost of 1  holiday paper be y.

Julie sold 13 rolls of plain wrapping paper and 8 rolls of holiday paper and earns $292.

Total Money earned by Julie is equal to sum of number of wrapping paper multiplied with cost of wrapping paper and number of holiday paper multiplied with cost of holiday paper.

So we can frame it in equation form as;

13x+8y=292\ \ \ \ \ equation\ 1

Now, Mark sold 7 rolls of plain wrapping paper and 2 rolls of holiday paper and earns $118.

Total Money earned by Mark is equal to sum of number of wrapping paper multiplied with cost of wrapping paper and number of holiday paper multiplied with cost of holiday paper.

So we can frame it in equation form as;

7x+2y=118\ \ \ \ \ equation\ 2

Now Multiplying equation 2 by 4 we get;

4(7x+2y)=118\times4\\\\4\times7x+4\times2y=118\times4\\\\28x+8y= 472 \ \ \ \ equation\ 3

Now Subtracting equation 1 from equation 3.

(28x+8y)-(13x+8y)= 472-292\\\\28x+8y-13x-8y= 180\\\\15x=180\\\\x=\frac{180}{2} = \$12

Now substituting the value of x in equation 1 we get;

13x+8y=292\\\\13\times12+8y=292\\\\156+8y=292\\\\8y=292-156\\\\8y=136\\\\y=\frac{136}{8}= \$17

Hence Cost of one roll of plain wrapping paper is $12 and Cost of one roll of holiday paper is $17.

8 0
4 years ago
One side of a rectangle is 20 cm larger than the other side. If you make the smaller side two times larger and the larger side t
grandymaker [24]
Let L be the length
Let w be the width
Let p be the perimeter
L+w+L+w=p
L=w+20
3L+2w+3L+2w=240
Sub the first equation in for L in the second equation and solve for w
3(w+20)+2w+3(w+20)+2w=240
3w+60+2w+3w+60+2w=240
10w+120=240
10w=240-120
10w=120
W=120/10
W=12
Sub w into the first equation and solve for L
L=w+20
L=12+20
L=32
Hope this helps!
3 0
4 years ago
Find the area of the surface. The helicoid (or spiral ramp) with vector equation r(u, v) = u cos v i + u sin v j + v k, 0 ? u ?
kifflom [539]
Fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
4 0
4 years ago
The area of a rectangular field is 48m2 and one of its sides is 6m . How long will a lady take to cross the field diagonally at
tatiyna

Answer:

It will take her approximately 28 seconds to cross the diagonal of the pitch

Step-by-step explanation:

If we can find the length of the diameter of the field (in Metres), we can easily find the time it takes her to cross this length using motion equations.

Step one: Find the length of the field from its area.

The field is rectangular in shape. The area of the field is 48m^2. To get the area of the field, we had to multiply its length and its breadth.

i.e area = length X breadth.

Let us assume that the breadth = 6m

its length will be area / breadth = 42/ 6 = 7m

The length of the pitch = 7 m

Step Two: Find the length of the diagonal using Pythagoras' theorem.

From Pythagoras'theorem, the length of the diagonal  can be obtained by

diagonal = \sqrt{l^2 +b^2}

diagonal = \sqrt{6^2+ 7^2}  = 9.22m

The length of the diagonal is 9.22m

Step three: Find the time using her speed and the distance she needs to cover.

Time = distance / speed

time = 9.22 /20 = 0.46 minutes

It will take her approximately 28 seconds to cross the diagonal of the pitch

6 0
3 years ago
Other questions:
  • 15 is 25 percent of what number
    7·1 answer
  • Write a compound inequality to represent all of the numbers between -4 and 6.
    12·1 answer
  • 16x^2-24x+7=0 equation and/or inequalities
    12·2 answers
  • Which statement best explains the relationship between lines FG and HJ they are perpendicular
    9·1 answer
  • Evaluate f(x) = 3x − 7 when x = 4.
    10·1 answer
  • 10 waffles and 4 pancakes cost $14. Five waffles and eight pancakes cost
    14·1 answer
  • You buy a calculator for $65 A 6% sales tax added.
    12·1 answer
  • Write an equation for the situation.
    15·1 answer
  • Please help I’m timed thank you!!!
    7·1 answer
  • What is the slope-intercept equation<br> for the following line?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!