Question

A jet travels 3800 miles against the wind in 5 hours and 4500 miles with the wind in the same amount of time. What is the rate ofthe jet in still air and what is the rate of the wind?miRate of the jet in still air:음DOХX5?miRate of the wind:OF

Answer 1

The rate of the jet in still air is 830mi/hr

The rate of the jet in the wind is 70mi/hr

Explanations:

Let the rate of the jet in still air be x

Let the rate of the jet in wind be y

The formula for calculating distance traveled is expressed as:

`\begin{gathered} \text{distance}=\text{speed}*\text{time} \\ d=st \end{gathered}`

If a jet travels 3800 miles against the wind in 5 hours, the rate of the jet will be expressed as:

`\begin{gathered} 3800=5(x-y) \\ x-y=760 \end{gathered}`

If the same jet travels 4500 miles with the wind in the same amount of time, the rate of the jet will be expressed as:

`\begin{gathered} 4500=5(x+y) \\ x+y=900 \end{gathered}`

Solve the equations simultaneously

x - y = 760

x + y = 900

Add both equations to have:

x + x = 760 + 900

2x = 1660

x = 1660/2

x = 830mi/hr

Since x - y = 760, hence;

y = x - 760

y = 830 - 760

y = 70mi/hr

Hence the rate of the jet in still air is 830mi/hr and the rate of the jet in the wind is 70mi/hr