Question

At maximum speed, an airplane travels2100 miles against the wind in 6 hours.Flying with the wind, the plane cantravel the same distance in 4 hours.Let x be the maximum speed of the plane andy be the speed of the wind. What is the speedof the plane with no wind?Enter the correct answer.DONE

Answer 1

Concept

Speed is the distance divide by time.

`\begin{gathered} \text{Speed = }\frac{dis\tan ce}{\text{time}} \\ \end{gathered}`
`\begin{gathered} x\text{ - y = }(2100)/(6) \\ x\text{ - y = 350 ----------------------- 1} \\ x\text{ + y = }(2100)/(4) \\ x\text{ + y = 525 -----------------------2} \end{gathered}`

Next, solve the two systems of equations to find the value of x and y.

From equation 1, make y subject of the formula and substitute in equation 2.

x - y = 350

x - 350 = y

Substitute, y = x - 350 in the equation 2.

x + x - 350 = 525

collect like terms

x + x = 525 + 350

2x = 875

Divide 2 on both side to get:

x = 875/2

x = 437.5

Final answer

The speed of the plane with no wind = 437.5