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Physics 101 Mechanics
4 days, 6 hours ago
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Two trains going in opposite directions leave at the same time. One train travels 15 mph faster than the other. In 6 hours, the trains are 630 miles apart. Find the speed of each.
Rational Equations and Problem Solving
we're told that two trains air going in opposite directions that they leave from the station. At the same time. We're told that one train travels 15 MPH faster than the other train. And we're told that in six hours the trains our 630 miles apart were asked to find the speed of each train. Understand this problem with Straw Table for the Rose? We have trained A and train B for the columns. We have the time that the trains travel in ours. We have the distance that the trains travel in miles, and we have the rate at which the trains travel, which is the distance over the time. We're told that these trains are going in opposite directions. Okay, so let's call. All right, so one train travels 15 MPH faster than the other. So let's say that train a traveling at a race x MPH. And let's suppose that training is the warm, just traveling 15 MPH faster than the other train that follows that trained. He is traveling at a rate of X minus 15 MPH. We're told that both trains travel for six hours and we had a distance between trains according to the rates. Well, this is going to be the rate times time. So the train a traveled six x file train D, will travel six times X minus 15 miles from a station. And now it's translate the problem into an equation. So we have that. So the trains are travelling in opposite direction. The total distance between the trains, which is distance training, travels six x plus the distance train be travels six times X minus 15 is equal to 630 sold. This equation we have by the distributive property this is equal to six x plus six x minus and then six times 15 which is 90 equals 6 30 And if we add like terms, we get 12. X minus 90 equals 6 30 By the addition property of equality, you have 12. X is equal to 6 30 plus 90 which is 7 20 by evil property of equality, we have that X is equal to 7 20 over 12 which is the same as 3 60 over six or 60. Check our answer. Substitute back into the equation. So we have it six times 60 plus six times 60 minus 15. This is equal to if you factor in a six six times 60 plus 60 minus 15. This is 1 20 minus 15. So six times 105 And this is equal to 630 which is what the right side is. Store answer is valid. And to state our answer recall that X was defined to be the rate at which training is traveling. And so we have that one train is traveling at 60 MPH, and the other train, which we defined its rate is X minus 15 is traveling at 60 miles 15 or 45 MPH.
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In mathematics, a proof is a sequence of statements given to explain how a conclusion is derived from premises known or assumed to be true. The proof attempts to demonstrate that the conclusion is a logical consequence of the premises, and is one of the most important goals of mathematics.
In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.
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