Question

a plane flies between two cities that are 1120 miles apart. when going with the wind, the plane makes the journey in7/4 hour(s). when going against the wind, it takes 2 hour(s).

Answer 1

The plane's speed is 600 mph and the wind's speed is 40 mph.

To solve this problem, we can use the formula:

Distance = Speed × Time

Let's denote the speed of the plane as V and the speed of the wind as W.

When the plane is flying with the wind, its effective speed will be increased, while when flying against the wind, its effective speed will be decreased.

1. Going with the wind:

The distance between the cities is 1120 miles, and the time taken is 7/4 hours. Using the formula, we have:

1120 = (V + W) × (7/4)

2. Going against the wind:

The distance between the cities is 1120 miles, and the time taken is 2 hours. Using the formula, we have:

1120 = (V - W) × 2

We now have a system of two equations with two variables (V and W). We can solve this system to find the values of V and W.

Solving equation 1:

1120 = (V + W) × (7/4)

1120 = (7V + 7W)/4

Multiply both sides by 4:

4480 = 7V + 7W

Solving equation 2:

1120 = (V - W) × 2

560 = V - W

We can rewrite equation 2 as:

V = 560 + W

Substitute this value of V into equation 1:

4480 = 7(560 + W) + 7W

4480 = 3920 + 7W + 7W

560 = 14W

W = 40 mph

Substitute this value of W into equation 2 to find V:

V = 560 + W

V = 560 + 40

V = 600 mph

Therefore, the speed of the plane is 600 mph and the speed of the wind is 40 mph.