Question

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only .9 hours. What is the plane's speed in still air, and how fast is the wind blowing?

Answer 1

The plane's speed in still air is 145 miles per hour and the wind speed is 55 miles per hour. These values are obtained by setting up equations based on the distances and times provided, and solving for the two unknowns.

Step-by-step explanation:

Finding Airplane Speed and Wind Speed

To find the plane's speed in still air and the wind speed, we can set up two equations based on the given distances and times.

Let's denote the plane's speed in still air as P and the wind speed as W. When the plane flies against the wind (from Fargo to Bismarck), its effective speed is P - W, and when it flies with the wind (from Bismarck to Fargo), its effective speed is P + W.

Using the formula distance = speed × time, we get:

180 miles = (P - W) × 2 hours (against the wind)

180 miles = (P + W) × 0.9 hours (with the wind)

From these equations, we can solve for P and W.

Against the wind: 180 = 2P - 2W

With the wind: 180 = 0.9P + 0.9W

Dividing the first equation by 2 and the second by 0.9, we have:

90 = P - W

200 = P + W

Adding these two equations gives us 290 = 2P, so the plane's speed in still air P is 145 miles/hour. Subtracting the first equation from the second gives us 110 = 2W, so the wind speed W is 55 miles/hour.

Answer 2

90 mi/h

Step-by-step explanation:

Calculate speed, distance, or time using the formula d = st, distance equals speed times time. The Speed Distance Time Calculator can solve for the unknown sdt value given two known values.

Time can be entered or solved for in units of seconds (s), minutes (min), hours (hr), or hours and minutes and seconds (hh:mm:ss).

To solve for distance use the formula for distance d = st, or distance equals speed times time.

distance = speed x time

Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour. If rate r is the same as speed s, r = s = d/t. You can use the equivalent formula d = rt which means distance equals rate times time.

distance = rate x time

To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.

speed = distance/time

To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

time = distance/speed

Plane speed in still air: 120mph

Wind speed: 30pmh

Speed of plane to Bismarck: 90mph

Speed of plane to Fargo: 150mph