Question

21) A plane traveled 504 miles each way to Rome and back. The trip there was with the wind. It took 6 hours. The trip back was into the wind. The trip back took 12 hours. What is the speed of the plane in still air? What is the speed of the wind?

Answer 1

To find the speed of the plane in still air and the speed of the wind, you can set up a system of equations using the formula: Distance = Speed × Time.

Let's denote the speed of the plane in still air as "P" (in miles per hour) and the speed of the wind as "W" (in miles per hour).

1. For the trip to Rome (with the wind), the equation is:

504 = (P + W) × 6

2. For the return trip (against the wind), the equation is:

504 = (P - W) × 12

Now, we have a system of two equations with two variables:

1. 6P + 6W = 504

2. 12P - 12W = 504

First, let's simplify the equations:

1. P + W = 84

2. 2P - 2W = 42

Now, you can use the method of substitution or elimination to solve for "P" and "W."

Let's use the elimination method. Multiply equation 1 by 2 to make the coefficients of "W" in both equations cancel out:

1. 2(P + W) = 2(84)

2. 2P + 2W = 168

Now, add equation 2 to the modified equation 1:

(2P + 2W) + (2P - 2W) = 168 + 42

Simplify:

4P = 210

Now, divide by 4 to solve for "P," the speed of the plane in still air:

P = 210 / 4

P = 52.5 mph

Now that we have the speed of the plane in still air (P), you can find the speed of the wind (W) by substituting this value into equation 1:

52.5 + W = 84

Subtract 52.5 from both sides:

W = 84 - 52.5

W = 31.5 mph

So, the speed of the plane in still air is 52.5 mph, and the speed of the wind is 31.5 mph.