Question

A pilot wants to arrive at her destination as soon as possible. Air traffic is busy, so she can take off 16 minutes later than expected and will be able to travel four times faster than expected if she waits. Create an equation to represent her total travel time, including wait time, where x is the number of minutes the flight was expected to take.

Answer 1

`(4)/(x)=(1)/(x-16)`

`21(1)/(3)\ \text{minutes}`

Explanation:

Let x be the number of minutes the flight was expected to take. Actually, the flight will take (x+16) minutes.

Let S be the distance to be covered.

Expected speed
`=(S)/(x)`

Actual speed
`=(S)/(x-16)` (shee will be flying 16 minutes less)

The pilot will be able to travel four times faster than expected if she waits, so

`4\cdot (S)/(x)=(S)/(x-16)\ \ \ \text{[Divide by S]}\\ \\(4)/(x)=(1)/(x-16)\ \ \ \text{[Cross multiply]}\\ \\4(x-16)=x\\ \\4x-64=x\\ \\4x-x=64\\ \\3x=64\\ \\x=(64)/(3)=21(1)/(3)\ \text{minutes}`