Question

Solving distance rate time problem using a system of linear

Answer 1

Step 1

Write a system of equations from the question.

Let x = speed of the plane in still air

y = speed of jetstream

`\begin{gathered} \text{Speed with jet}stream=x+y \\ \text{Speed }against\text{ jetstream=x-y} \end{gathered}`
`\begin{gathered} \text{Distance}=rate(\text{time)} \\ \text{Time therefore=}\frac{\text{Distance}}{\text{rate}} \end{gathered}`

For the first instance with the jetstream;

`\begin{gathered} (6296)/(x+y)=8 \\ 6296=8(x+y)---(1) \end{gathered}`

For the second instance against the jetstream;

`\begin{gathered} (5416)/(x-y)=8 \\ 5416=8(x-y)---(2) \end{gathered}`

Step 2

Solve for x. Add equation 1 to 2

`\begin{gathered} 6296=8x+8y---(1) \\ 5416=8x-8y---(2) \\ 11712=16x \\ (16x)/(16)=(11712)/(16) \\ x=732\text{miles per hour} \end{gathered}`

Step 3

Solve for y

Substitute for x in equation 1

`\begin{gathered} 6296=8(732)+8y \\ 6296=5856+8y \\ 6296-5856=8y \\ 440=8y \\ (8y)/(8)=(440)/(8) \\ y=55\text{ miles per hour.} \end{gathered}`

Rate of the jet in still air=732miles per hour

Rate of the jetstream=55 miles per hour