Question

A train travels at `110 3/10` miles per hour. At this rate, how far will the train travel in `2 1/2` hours?

Answer 1

`1103/4color(white)(i)"miles"color(white)(i)orcolor(white)(i)275.75color(white)(i)"miles"`

Explanation:

Recall that the formula for distance is:

`color(blue)(|bar(ul(color(white)(a/a)d=stcolor(white)(a/a)|)))`

where:
`d=`distance
`s=`speed
`t=`time

`1`. To determine how far the train will travel, start by converting the given mixed fractions into improper fractions.

`color(darkorange)110` `color(turquoise)3/color(violet)10color(white)(XXXXXXXXXXX)color(darkorange)2` `color(turquoise)1/color(violet)2`

`=(color(violet)10color(darkorange)(xx110)color(white)(i)color(turquoise)(+3))/color(violet)10color(white)(XXXXX)=(color(violet)2color(darkorange)(xx2)color(white)(i)color(turquoise)(+1))/color(violet)2`

`=(1100+3)/10color(white)(AXXXXxxii)=(4+1)/2`

`=1103/10color(white)(XXXXXXXxxx)=5/2`

`2`. Substitute your known values into the distance formula.

`d=st`

`d=(1103/10)(5/2)`

Don't forget about units! Note that `"miles"/"hour"` is read as "miles per hour."

`d=((1103color(white)(i)"miles")/(10color(white)(i)"hour"))((5color(white)(i)"hours")/2)`

`3`. Since `5` (numerator) and `10` (denominator) can be divided by a common factor of `5`, their values can be reduced.

`d=((1103color(white)(i)"miles")/(10color(red)(-:5)color(white)(i)"hour"))((5color(red)(-:5)color(white)(i)"hours")/2)`

`d=((1103color(white)(i)"miles")/(2color(white)(i)"hour"))((1color(white)(i)"hours")/2)`

`4`. Cancel out the unit, hour(s), which appear in the numerator and denominator as a pair.

`d=((1103color(white)(i)"miles")/(2color(white)(i)color(red)cancelcolor(black)("hour")))((1color(white)(i)color(red)cancelcolor(black)("hours"))/2)`

`5`. Solve.

`color(green)(|bar(ul(color(white)(a/a)d=1103/4color(white)(i)"miles"color(white)(i)orcolor(white)(i)275.75color(white)(i)"miles"color(white)(a/a)|)))`