Ask question

Ask question

All categories

4 years ago

14

A passenger train traveled 180 miles in the same amount of time it took a freight train to travel 120 miles. The rate of the fre

ight train was 15 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train.

1 answer:

Mnenie [13.5K]4 years ago

5 0

Answer:

The passenger train is moving at 45 miles per hour

Step-by-step explanation:

Let the amount of time it took the two trains to travel the distance = t.

Since the two trains traveled the distance at the same time,

Rate of the passenger train = $\frac{180}{t}$

Rate of the freight train = $\frac{120}{t}$

<em>Where t is in hours.</em>

From the problem, we can see that the rate of the freight train was 15 miles per hour slower than the rate of the passenger train. Mathematically, we can represent this as

$\frac{120}{t}= \frac{180}{t}-15$

from the above equation, we can now get our value for t as

$\frac{120-180}{t}=-15\\\frac{-60}{t}=-15\\t=4 hours$

We have our time of travel for the two trains as 4 hours.

The rate of the passenger train can now be calculated by 180/4 = 45 miles per hour

You might be interested in

The average weight per adult is 150 pounds, and the average weight per child is 40 pounds . The maximum weight is 1,500 pounds.

AnnZ [28]

With the ten children already in the elevator, the weight is at 400 pounds. Therefore you have 1,100 pounds before reaching the maximum weight. So about 7 adults can get in.

8 0

3 years ago

Read 2 more answers

Find the sum of the polynomials.<br>x² + 5x² + 9x - 6<br>9x² - 4x + 6

igomit [66]

Answer:

15x^2+5x

Step-by-step explanation:

If adding both together, this is your answer.

Hope this helps!

4 0

3 years ago

Read 2 more answers

"A student made the following chart to prove that AB2 + BC2 = AC2.

katovenus [111]

Step 3 has an error.

Step-by-step explanation:

Similarity-criteria of triangles:

1. All the corresponding angles of two triangles should be equal.

2. The ratio between the corresponding sides of two triangles should be equal.

In $\triangle ABC$ and $\triangle BDC$

$\angle BAC = \angle DBC \\\angle ACB = \angle BCD$

All the angles of triangle are equal.

∴ $\triangle ABC \sim \triangle BDC$

Since, $\triangle ABC \sim \triangle BDC$

$\frac{AC}{BC}=\frac{AC}{DC}$

$BC^{2}=AC \times DC$

In $\triangle ABC$ and $\triangle BDA$ ,

$\fbox{\begin\\ \angle ABC= \angle BDA = 90^{\circ}\end{minispace}}$

$\fbox{\begin \\\angle BAC = \angle BAD\\\end{minispace}}$

$\angle ACB = \angle ABD$

All the angles of triangle are equal.

∴ $\fbox{\begin\triangle ABC \sim \triangle BDA \end{minispace}}$

∵ $\triangle ABC \sim \triangle BDA$

$\frac{AC}{AB}=\frac{AB}{AD}$

$AB^{2}=AC \times AD$

Now, $AB^{2}+BC^{2}$ can be simplified as,

$AB^{2}+BC^{2}=AC \times AD+AC \times DC\\AB^{2}+BC^{2}=AC(AD+DC)\\AB^{2}+BC^{2}=AC(AC)\\AB^{2}+BC^{2}=AC^{2}$

Learn more:

1. Find the height of the triangle?

brainly.com/question/12989306

2. Which undefined term is needed to define an angle? brainly.com/question/3717797

3. Look at the figure, which trigonometric ratio should you use to find x? brainly.com/question/9880052

Answer Details

Grade: Junior High School

Subject: Mathematics

Chapter: Triangle

Keywords: triangle, similar, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs

8 0

3 years ago

Five roses cost $25 how many Roses can you purchase for $75

Radda [10]

Answer: 15

Step-by-step explanation: 5 roses are 25 dollars so what your going to do is multiply 5 by 3 to get 15 do the same with 25, 25 x 3 is 75 so you will get 15 roses for 75 dollars

8 0

3 years ago

Kayla bought 5.5 pounds of apples. She paid a total of $7.15. What was the unit rate of the apples per pound? Answer and explica

Bess [88]

Answer:

$1.30/pound

Step-by-step explanation:

7.15/5.5=1.3, and 1.3 x 5.5= 7.15

6 0

3 years ago