Ask question

Ask question

All categories

3 years ago

11

"A passenger train traveled 100 miles in the same amount of time it took a freight train to travel 90 miles. The rate of the fre

ight train was 10 miles per hour slower than the rate of the passenger train. Find the rate of the passenger train."

1 answer:

Pavel [41]3 years ago

7 0

Answer: the rate of the passenger train is 100 mph.

Step-by-step explanation:

Let x represent the rate of the passenger train.

The rate of the freight train was 10 miles per hour slower than the rate of the passenger train. It means that the rate of the freight train is (x - 10) mph

The passenger train traveled 100 miles. It means that the time it took travel 100 miles is

100/x

In the same amount of time, it took a freight train to travel 90 miles. It means that the time it took travel 90 miles is

90/(x - 10)

Since the time is the same, then

100/x = 90/(x - 10)

Cross multiplying, it becomes

100(x - 10) = 90x

100x - 1000 = 90x

100x - 90x = 1000

10x = 1000

x = 100 mph

You might be interested in

Solve each inequality, and then drag the correct solution graph to the inequality.

Nesterboy [21]

The correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

(NOTE: The graphs are labelled A, B and C from left to right)

For the first inequality,

$4(9x-18)>3(8x+12)$

First, clear the brackets,

$36x-72>24x+36$

Then, collect like terms

$36x-24x>36+72\\12x >108$

Now divide both sides by 12

$\frac{12x}{12} > \frac{108}{12}$

∴ $x > 9$

For the second inequality

$-\frac{1}{3}(12x+6) \geq -2x +14$

First, clear the fraction by multiplying both sides by 3

$3 \times[-\frac{1}{3}(12x+6)] \geq3 \times( -2x +14)$

$-1(12x+6) \geq -6x +42$

Now, open the bracket

$-12x-6 \geq -6x +42$

Collect like terms

$-6 -42\geq -6x +12x$

$-48\geq 6x$

Divide both sides by 6

$\frac{-48}{6} \geq \frac{6x}{6}$

$-8\geq x$

∴ $x\leq -8$

For the third inequality,

$1.6(x+8)\geq 38.4$

First, clear the brackets

$1.6x + 12.8\geq 38.4$

Collect likes terms

$1.6x \geq 38.4-12.8$

$1.6x \geq 25.6$

Divide both sides by 1.6

$\frac{1.6x}{1.6}\geq \frac{25.6}{1.6}$

∴ $x \geq 16$

Let the graphs be A, B and C from left to right

The first graph (A) shows $x\leq -8$ and this matches the 2nd inequality

The second graph (B) shows $x \geq 16$ and this matches the 3rd inequality

The third graph (C) shows $x > 9$ and this matches the 1st inequality

Hence, the correct solution graph to the inequalities are

$4(9x-18)>3(8x+12)$ → C

$-\frac{1}{3}(12x+6) \geq -2x +14$ → A

$1.6(x+8)\geq 38.4$ → B

Learn more here: brainly.com/question/17448505

8 0

2 years ago

Find f(t – 3) for f(x) = 4x^2 – 8x + 4.

Vladimir79 [104]

Answer:

<h2>A. 4t² - 32t + 64</h2>

Step-by-step explanation:

Instead of x put (t - 3) in the equation of the function f(x) = 4x² - 8x + 4:

f(t - 3) = 4(t - 3)² - 8(t - 3) + 4

<em>use (a - b)² = a² - 2ab + b² and the distributive property a(b + c) = ab + ac</em>

f(t - 3) = 4(t² - (2)(t)(3) + 3²) + (-8)(t) + (-8)(-3) + 4

f(t - 3) = 4(t² - 6t + 9) - 8t + 24 + 4

f(t - 3) = (4)(t²) + (4)(-6t) + (4)(9) - 8t + 28

f(t - 3) = 4t² - 24t + 36 - 8t + 28

f(t - 3) = 4t² + (-24t - 8t) + (36 + 28)

f(t - 3) = 4t² - 32t + 64

3 0

3 years ago

4h+8=20 what is h?..........

sergey [27]

I believe it's 3 because 4 times 3 equals 12 and 12 plus 8 equals 20!
4(3)+8=20

Hoped this helped! :)

3 0

3 years ago

Read 2 more answers

You fill 1/4 of a 5 gallon bucket. how many more gallons of water will you need to fill the bucket

Bess [88]

1/4 of a five gallon bucket is 1 1/4 gallons.

5-1 1/4=3 3/4 gallons left to fill.

Answer: 3 3/4 gallons

8 0

3 years ago

If a person gets paid $290 a load and receive 5% increase on top of that, how much more is he getting paid?

lesya [120]

That person is getting $14.50 more. Since he gets a 5% increase from the set $290, you must multiply .05 (the percentage) with 290 (that person's original load payment). When you do so, you get $14.50 and that would be how much more the person is getting paid.

8 0

3 years ago