Question

A motor makes 5256.75 complete rotations in 4.89 minutes. How would you calculate the number of degrees the motor rotates in 21.6 seconds?

Answer 1

See a solution process below:

Explanation:

First, we can write the expression in the problem as:

`(5256.75"rotations")/(4.89"min")`

Next, we can convert rotations to degrees. 1 rotation is equation to `360^o`. We can multiply the fraction by 1 to convert to degrees without changing the value of the fraction:

`(5256.75"rotations")/(4.89"min") xx 360^o/(1"rotation") =>`

`(5256.75color(red)(cancel(color(black)("rotations"))))/(4.89"min") xx 360^o/(1color(red)(cancel(color(black)("rotation")))) =>`

`(5256.75 xx 360^o)/(4.89"min") =>`

`(1892430^o)/(4.89"min")`

Then we can convert minutes to seconds. 1 minute is 60 seconds. We can again multiply the fraction by 1 to convert to degrees without changing the value of the fraction:

`(1892430^o)/(4.89"min") xx (1"min")/(60"sec") =>`

`(1892430^o)/(4.89color(red)(cancel(color(black)("min")))) xx (1color(red)(cancel(color(black)("min"))))/(60"sec") =>`

`(1892430^o)/4.89 xx 1/(60"sec") =>`

`(1892430^o)/(293.4"sec") =>`

`(6450^o)/("sec")`

To find the number of degree the motor rotates in 21.6 seconds we can yet again multiply our fraction by the appropriate form of `1`:

`(6450^o)/("sec") xx 21.6/21.6 =>`

`(6450^o xx 21.6)/(21.6"sec") =>`

`(139320^o)/(21.6"sec")`

The motor rotates 139,320 degrees in 21.6 seconds.