5.5 Application ii - solving problems  (Page 4/4)

One number is fifteen more than another number. The sum of the two numbers is 27. What are they?

The length of a rectangle is 6 meters more than three times the width. The perimeter of the rectangle is 44 meters What are the dimensions of the rectangle?

Seven is added to the product of 41 and some number. The result, when divided by four, is 63. What is the number?

The second side of a triangle is five times the length of the smallest side. The third is twice the length of the second side. The perimeter of the triangle is 48 inches. Find the length of each side.

Person A is four times as old as person B, who is six times as old as person C, who is twice as old as person D. How old is each person if their combined ages are 189 months?

Two consecutive odd integers sum to 151. What are they?

Three consecutive integers sum to 36. What are they?

Three consecutive even integers add up to 131. What are they?

As a consequence of Einstein’s theory of relativity, the rate of time passage is different for a person in a stationary position and a person in motion. (Hard to believe, but true!) To the moving observer, the rate of time passage is slower than that of the stationary observer, that is, the moving person ages slower than the stationary observer. (This fact has been proven many times by experiments with radioactive materials.) The effect is called “time dilation” and is really only noticeable when an object is traveling at near the speed of light (186,000 miles per second). Considering these ideas, try to solve the following problems:

Two people have identical clocks. One is standing on the earth and the other is moving in a spacecraft at $95\%$ the speed of light, 176,700 miles per second. The moving person’s rate of time passage at this speed is about $0.31$ times as fast as the person standing on earth.

1. If two days of earth time pass, how many days actually pass on the spacecraft?
2. If 30 years of earth time pass, how many years have actually passed on the spacecraft?
   5. years have passed on the spacecraft.
3. If 30 years have passed on the spacecraft, how many years have passed on the earth?
4. A space traveler makes a round-trip voyage to the star Capella. The trip takes her 120 years (traveling at 176,000 miles per second). If it is the year 2000 on earth when she leaves, what earth year will it be when she returns?

( [link] ) Specify the domain of the equation $y=\frac{x-1}{x+4}$ .

( [link] ) Classify the equation $x+4=1$ as an identity, a contradiction, or a conditional equation.

( [link] ) Classify the equation $2x+3=2x+3$ as an identity, a contradiction or a conditional equation.

( [link] ) Solve the equation $4(x-1)+12=-3(2x+4)$ .

( [link] ) Translate the following sentence to a mathematical equation. Three less than an unknown number is multiplied by negative four. The result is two more than the original unknown number.