Question

A private jet can fly 2704 miles in four hours with a tailwind, but only 2408 miles in four hours with a headwind.What is the speed of the jet in still air?What is the speed of the wind?

Answer 1

The Solution:

Let the speed without the tailwind (wind) be represented with x.

And let the speed of the wind be represented with y.

The Speed without wind:

Given that a jet can only fly 2408 miles in 4 hours.

By formula,

$S=\frac{D}{T}$

Where,

D = distance = 2408 miles

T = time = 4 hours

S = (x - y) miles/hour

Substituting these values in the formula, we get

$\begin{gathered} x-y=\frac{2408}{4} \\ \text{ Cross multiplying, we get} \\ 4(x-y)=2408 \end{gathered}$

Dividing both sides by 4, we get

$x-y=602\ldots\text{eqn}(1)$

Similarly,

The Speed with the wind:

Given that the jet fly 2704 miles in 4 hours with a tailwind.

Again, the formula:

$S=\frac{D}{T}$

Where,

D = distance = 2704 miles

T = time = 4 hours

S = (x + y) miles/hour

Substituting these values in the formula, we get

$\begin{gathered} x+y=\frac{2704}{4} \\ \\ x+y=676\ldots\text{eqn}(4) \end{gathered}$

Solving both equations as simultaneous equations.

$\begin{gathered} x-y=602\ldots\text{eqn}(1) \\ x+y=676\ldots\text{eqn}(2) \end{gathered}$

By the elimination method, we shall add their corresponding terms together in order to eliminate y.

$\begin{gathered} x-y=602 \\ x+y=676 \\ -------- \\ 2x=1278 \end{gathered}$

Dividing both sides by 2, we get

$x=\frac{1278}{2}=639\text{ m/h}$

Thus, the speed of the jet in still air (without wind) is 639 miles/hour.

To solve for y:

We shall substitute 639 for x in eqn(2)

$\begin{gathered} x+y=676 \\ 639+y=676 \end{gathered}$

Collecting the like terms, we get

$y=676-639=37\text{ m/h}$

Therefore, the speed of the wind is 37 miles/hour.