Question

An airplane travels 1152 miles in 4 hours, going against the wind. The return trip is with the wind, and takes only 3.2 hours. Find the rate of the airplane with no wind. Find the rate of the wind.

Answer 1

The Solution:

Let the rate with no wind be represented with x.

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

Given:

With no wind:

distance (d) = 1152 miles

time (t) = 4 hours

rate with no wind = x-y

By formula,

`\text{ speed (s) = Rate =}\frac{\text{ distance(d)}}{\text{time(t)}}`

Substituting these values, we get

`\begin{gathered} x-y=(1152)/(4)=288\text{ m/h} \\ \\ x-y=288\ldots eqn(1) \end{gathered}`

Finding the rate with the wind:

distance = 1152 miles

time(t) = 3.2 hours

rate = x+y

Substituting these values, we get

`\begin{gathered} \text{ rate =}\frac{\text{ distance (d)}}{\text{ time (t)}} \\ \\ x+y=(1152)/(3.2)=360\text{ m/h} \\ \\ x+y=360\ldots\text{eqn}(2) \end{gathered}`

Solving the pair of equations simultaneously, we get

`\begin{gathered} x-y=288 \\ x+y=360 \end{gathered}`

By the Elimination Method, we shall add the corresponding terms in both equations.

`2x=648`

Dividing both sides by 2, we get

`\begin{gathered} x=(648)/(2)=324 \\ \\ x=324\text{ m/h} \end{gathered}`

Thus, the rate of the airplane with no wind is 324m/h.

To find the rate of the wind:

We shall substitute 324 for x in eqn(2).

`\begin{gathered} 324+y=360 \\ \text{collecting the like terms, we get} \\ y=360-324 \\ y=36\text{ m/h} \end{gathered}`

Therefore, the rate of the airplane with no wind is 324m/h.

The rate of the wind is 36 m/h.