Question

Two airplanes left the same airport traveling in opposite directions. If one airplane averages 400 miles per hour and the other airplane averages 250 miles per hour, in how many hours will the distance between the two planes be 1625 miles?

Answer 1

Time taken `=2 1/2" hours"`

Explanation:

Did you know you can manipulate units of measurement
in the same way you do numbers. So they can cancel out.

distance = speed x time

The speed of separation is 400 + 250 = 650 miles per hour

Note that 'per hour' means for each of 1 hour

The target distance is 1625 miles

distance = speed x time `->color(green)( 1625" miles" = (650color(white)(.) "miles")/("1 hour")xx"time")`

`color(white)("d")`

`color(white)("d")`

Multiply both sides by `color(red)(("1 hour")/(650color(white)(.) "miles"))`. This turnes the `(650color(white)(.) "miles")/("1 hour")` on the right of the = into `color(purple)( 1)`

`color(white)("d")`
`color(white)("d")`

`color(white)("dddddddddddddd") color(green)(-> 1625 cancel(" miles")color(red)(xx("1 hour")/(650color(white)(.) cancel("miles"))) = color(purple)(1)xx"time")`

`color(white)("dddddddddddddd") color(green)(-> color(white)("d") 1625/650" hours" =" time")`

Time taken `=2 1/2" hours"`