An airplane travels 1900 km at a speed of 720 km/h, and then e...

Question

An airplane travels 1900 km at a speed of 720 km/h, and then encounters a tailwind that boosts its speed to 990 km/h for the next 2700 km. What was the total time for the trip? What was the average speed of the plane for this trip? [Hint: Does Eq. 2–12d apply?]

Accepted Answer

Hey, everyone in this problem, we're asked to consider a train that initially travels 1.5 multiplied by 10 to the exponent three miles at a speed of 180 MPH, then reduces its speed to 120 MPH for the subsequent three multiplied by 10 to the exponent. Three miles are asked to do two things. The first is to find the journey's total duration and the second is to find the train's average speed in MPH for the entire trip. Now, we're given four different answer choices. Ok. For part one, we have the duration could either be 33.3 hours or 25.3 hours. For the average speed we have that it could be 135 miles or 150 miles. Ok. So two answer choices for each of the two parts of our problem. When we combine those all together, we get four different options for our answer choices and we'll come back to those as we work through this problem. So starting with part one and in part one, we're asked to determine the total duration. So the total duration we're gonna call that t the total time and that's just gonna be equal to the time from segment. What, what's the time from segment two? OK. We have these two different segments where we're going a different distance we're traveling at different speed and that's gonna allow us to calculate that time. Now, let's recall the relationship between the speeds, the distance and the time I recall that the speed V is equal to the distance divided by the time. And so if we wanna calculate the time, we can rearrange this equation and write that the time is gonna be the distance divided by the speed. All right. So for T one, OK, the time for segment one, we're told that we travel 1.5 multiplied by 10 to the exponent three miles. So T one is gonna be 1.5 multiplied by 10 to the exponent three miles divided by the time which we're told or sorry, divided by the speed, which we're told is 180 MPH. The time is what we're looking for. All right. So we have 1.5 multiplied by 10 to the exponent three miles divided by 100 and 80 MPH. The unit of miles is gonna divide out, we're gonna be left with the unit of hours. Let me get that. T one is 8.333 repeated hours. All right, we're gonna do the same for T two. Now, for T two, we're told that it reduces the speed to 100 and 20 MPH and travels three multiplied by 10 to the exponent three miles. So T two is going to be three multiplied by 10 to the exponent, three miles divided by 120 MPH. Ok. What you'll notice is that in this second segment, we're traveling a further distance, we're going a slower speed. So the time it takes is going to be longer and we get that T two is 25 hours. All right. So we have these two intermediate times the time it takes for each segment. Remember, we're looking for that total duration. So we wanna add these times up. So we get that the total duration. T one plus T two is gonna be 8.333 repeated hours plus 25 hours, which gives us a total time of 33.33 repeated hours. Right? Let's take a look at our answer choices and see if we can narrow anything down at this point. Option. A and B both have that duration being 33.3 hours. So those are possible answers. C and D have it being 25.3 hours. So that's not correct. So we can eliminate C and D. Now we're gonna move to part two to finish this problem off. And part two is asking us to find the train's average speed for the entire journey. Ok. So recall that the average speed is going to be equal to the total distance divided by the total time. Now, the total time or the duration we just calculated. Ok. So that's going to be our T value from part one, the total distance we can calculate, we know how far we travel in segment one, we know how far we travel in segment two to find the total distance we travel. We just need to add them up. And so our average speed is going to be 1.5 multiplied by 10 to the exponent three miles. Ok. So the distance of the first segment plus three multiplied by 10 to the exponent three miles distance of the second segment that gives us our total distance. And we're gonna divide that by our total time which we found to be 33.33 repeated hours. Hm When we work this out, we get that average speed is going to be equal to 135 MPH. All right. And that's it. For part two, let's head back up to our answer choices. We had narrowed it down to option A or option B. Option B has that. The average speed is 150 MPH. That is not correct. And so we are left with option A which has the correct answer for both parts and has that the duration is 33.3 hours and the speed is 135 MPH. Thanks everyone for watching. I hope this video helped see you in the next one.

An airplane travels 1900 km at a speed of 720 km/h, and then encounters a tailwind that boosts its speed to 990 km/h for the next 2700 km. What was the total time for the trip? What was the average speed of the plane for this trip? [Hint: Does Eq. 2–12d apply?]

Key Concepts

Speed and Velocity

Average Speed

Kinematic Equations

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