Problem

Uniform motion problems. A husband and wife work …

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Problem 30 Easy Difficulty

Uniform motion problems.
Two remotely controlled unmanned aircraft are launched in opposite directions. One flies east at 78 mph and the other west at $82 \mathrm{mph}$. How long will it take the aircraft to fly a combined distance of 560 miles?

Answer

The time taken for a combined flight of 560 miles $=3.5$ hours

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Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

problem. 30 reads to remotely controlled Unmanned aircraft are launched in opposite directions. One flies east as 78 miles per hour and the other west at 82 miles per hour. How long will it take the aircraft if I combined distance of 560 miles. So to solve this problem, we're gonna make a chart one showing the east aircraft one representing the West aircraft. And since it's a uniform motion problem, we're going to use the equation. And times T is equal to D, which stands for a rate. Times time is equal to distance, and then the total distance between aircraft is 560 miles, so we're gonna fill that in as well. So far, 160 miles is the total distance. The aircraft traveling east is going 78 miles per hour. The aircraft traveling west is going 82 miles per hour. We don't know what the time is, so that's what we're trying to figure out. So we're gonna use T to represent both because it's gonna be the same amount of time. And then to find our distance, we're gonna have to multiply the rate times of time. So for the East aircraft, it's the distance is 70 80 and for the West aircraft, it's 82 t and we know that together the distance has to be equal to 560. So now we're gonna write an equation that includes the distance for both aircraft. So we have 78 t plus 82 t is equal to 560 from here. We're gonna add our like terms of 78 plus 82 is 160. So we have 160 t is equal to 560 and then from here, we're gonna have to isolate the very bold T. So we're gonna have to divide both sides by 160. So 160 divided by 160 is one. So we're left with just tea and then we have 560 divided by 160 which is 3.5, and our unit, for a time in this case is gonna be ours because our rate was miles per hour and our distance uses the unit of miles. So our time must be ours, and that is our solution

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