I am having trouble with this motion problem.A jet travels 1,890 miles in 3 hours. flying against the same wind,the plane makes a return trip in 3 1/2 hours.Find the wind speed and the plane`s airspeed.My book gives the answer,but I just can not understand the concept of how they get the problem.Thanks for any help I can get.
(V+W)3=1890
(V-W)3.5=1890
divide the top equation by 3, and the second equation by 3.5
V+W=630
V-W=540
add the equations
2V=1170
solve for V, W
Take if from here.
Sure, I can help you understand how to solve this motion problem. Let's break it down step by step.
The first thing we need to understand is the concept of speed = distance/time. In this problem, the speed of the jet is actually the combination of two different speeds - the speed of the plane in still air (which we'll call "airspeed") and the speed of the wind.
Let's use variables to represent the airspeed and the wind speed. We'll use "A" for the airspeed and "W" for the wind speed.
Now, let's consider the first trip where the jet travels 1,890 miles in 3 hours. We'll call this trip "Trip 1".
During Trip 1, the jet is flying with the wind, which means that the effective speed of the jet will be the sum of the airspeed and the wind speed. So, we can write the equation for Trip 1 as:
1,890 = (A + W) * 3
Now, let's consider the second trip where the jet makes a return trip in 3 1/2 hours. We'll call this trip "Trip 2".
During Trip 2, the jet is flying against the wind, which means that the effective speed of the jet will be the difference between the airspeed and the wind speed. So, we can write the equation for Trip 2 as:
1,890 = (A - W) * 3.5
Now we have a system of two equations with two unknowns (A and W).
To solve these equations, we can use a method called substitution. We'll solve the first equation for A and then substitute it into the second equation.
From the first equation, we can solve for A by dividing both sides by 3:
(A + W) = 1,890 / 3
A + W = 630
Now we substitute this value of A into the second equation:
(Before substitution) 1,890 = (A - W) * 3.5
(After substitution) 1,890 = (630 - W) * 3.5
Now we can simplify and solve for W:
1,890 = 2205 - 3.5W
-315 = -3.5W
W = -315 / -3.5
W = 90
Now that we have the wind speed (W = 90), we can substitute this value back into one of our original equations to find the airspeed (A).
(Using the first equation) A + 90 = 630
A = 630 - 90
A = 540
So the airspeed of the plane is 540 mph and the wind speed is 90 mph.
I hope this explanation helps clarify the steps to solve the problem. Let me know if you have any further questions!