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Boston and New York are approximately 280 miles apart. One train leaves Boston traveling towards New York at an average speed of 80 mph. Another train leaves New York at the same time traveling toward Boston at an average speed of 60 mph. (a) How long will it take them to meet. (b) How far has each train traveled when they meet?

(a) 2 hrs(b) $160 \mathrm{mi}, 120 \mathrm{mi}$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

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we have the following problem where Boston and New York are 280 miles apart. And we have a train that departed from Boston to New York, traveling at an average speed of 80 MPH and train from New York to Boston, traveling at about 60 MPH and both trains leave at the same time. And then this equation, we're gonna basically use of the equation because our unknown value, it's gonna be raised to the power of one. We're gonna use addition and subtraction toe under each other and multiplication and division two under each other. Okay, so we know that Boston, New York are 280 miles apart. So what we wanted to in this equation some chili is that we know that they both started at the same time. So we're able to use both the average speeds to begin with. So we're gonna have 80 times teeth. Class six. Thanks, Pete equals the total distance between them between Boston and New York. So we have essentially what we have right here said we're gonna be able to find at what time they'll be able to meet each other if we take their average speed and multiply it by the time that they will meet, assuming that Boston and New York are 280 miles apart. So for this one, which is gonna add both 80 times T plus 60 times t so it could be 140 extinct. It's equal to 80. So all right, here we just simplified it and just simply added them. So right. So now we're able to divide the left side of the equation by 140. Thank you. It's a great sees. I want to buy the right side of the equation. Also by 140 right? So now we're gonna be left with teeth because under 40 divided by 100 forties, just one. He was 280 divided by under 40. It's something that's cool. Four hours. So in this case, um, the trains they're gonna meet up will eventually meet up in two hours. And then the second part of the question is telling us how far has each drain traveled? So the train from Boston, just to notice speed train from Boston is maybe 80 MPH times two hours, just 160 miles. Then the train from New York, which will just be noticed and traveling at 60 MPH, thanks to our something it up for 220 miles together these off these miles at up to 280 miles. So this is our final answer. They meet up in two hours, and the train from Boston to New York traveled 260 miles in the train from New York to Boston, traveled 120 miles.

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