Question

a light aircraft travels 9 miles per hour less than twice the speed of a car. If a car can travel 112 miles in the same time it takes the aircraft to travel 206 miles, then what is the average speed of both?

Answer 1

Let the speed of a car = v

Distance travel by car = 112 miles

Speed of a light aircraft = 2v - 9

Distance travel by light aircraft = 206 miles

From time formula

`\text{Time = }\frac{Dis\tan ce}{\text{Speed}}`

Time for car

`\text{Time = }(112)/(v)`

Time for light aircraft

`Time\text{ = }\frac{206}{2v\text{ - 9}}`

Since the time is equal for both car and light aircraft

Therefore,

`\begin{gathered} (112)/(v)\text{ = }\frac{206}{2v\text{ - 9}} \\ \text{Cross multiply} \\ 206v\text{ = 112(2v - 9)} \\ 206v\text{ = 224v - 1008} \\ 1008\text{ = 224v - 206v} \\ 1008\text{ = 18v} \\ v\text{ =}(1008)/(18) \\ v\text{ = 56 miles per hour} \end{gathered}`

The average speed of a car = 56 miles per hour

The average speed of a light aircraft = 2v - 9

= 2(56) - 9

= 112 - 9

= 103 miles per hour