Question

Airplanes usually by faster from west to east in from east to west, because the prevailing winds go from west to east. The air distance between Chicago and London is about 4000 miles or the air distance between New York and London is about 3500 miles if Jack can fly eastbound from Chicago to London, the same time I can fly westbound wanted to New York and 35 mph winds. What’s the rate of the plane still there?

Answer 1

To solve the problem, we can set up an equation involving the rate of the airplane, wind speed, distance, and time.

Let's define:

- \( r \) = the speed of the plane in still air (in mph).
- The wind speed is given as 35 mph.

1. **Flying Eastbound (from Chicago to London):**
The effective speed of the plane when flying eastbound is \( r + 35 \) mph.
The distance is 4000 miles.
The time taken to fly from Chicago to London can be expressed as:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{4000}{r + 35}
\]

2. **Flying Westbound (from London to New York):**
The effective speed of the plane when flying westbound is \( r - 35 \) mph.
The distance is 3500 miles.
The time taken to fly from London to New York can be expressed as:
\[
\text{Time} = \frac{3500}{r - 35}
\]

Since both flights take the same amount of time, we can set the two time equations equal to each other:
\[
\frac{4000}{r + 35} = \frac{3500}{r - 35}
\]

Now we can cross-multiply to eliminate the fractions:
\[
4000(r - 35) = 3500(r + 35)
\]

Expanding both sides:
\[
4000r - 140000 = 3500r + 122500
\]

Now, let's bring all terms involving \( r \) to one side and constant terms to the other:
\[
4000r - 3500r = 122500 + 140000
\]
\[
500r = 262500
\]

Now, solve for \( r \):
\[
r = \frac{262500}{500} = 525
\]

Thus, the speed of the plane in still air is \( \boxed{525} \) mph.