Question

How far could a rabbit run if it ran 36km/h for 5.0min?

Answer 1

Distance = (speed) x (time)

The question GIVES us both the speed and the time.  Sadly, though, in order to work with them, we need them to both have the same units, but the information we're given has two different units for time:  

The speed is in (km per HOUR), but the time is in MINUTES.  We'll have to change one or the other before we can multiply them.

Well, 5.0 minutes is (5/60) = 1/12 of an hour.  We can use that.

Distance = (36 km/hr) x (1/12 hour)

Distance = (36/12) (km-hr/hr)

Distance = 3 km .

= = = = = = = = = =

There's a slightly different way to handle it.  If the problem was more complicated, this way would actually turn out to be a better way, and you'd have LESS chance of making a mistake if you did it this way:

Distance = (36 km/hr) x (5.0 min)

Distance = (36 x 5)  km - min / hr

Distance = 180 km · min / hr

This is a correct answer, but the unit is awkward.  We can change the unit at THIS point in our calculation.  All we have to do is multiply the answer by ' 1 ' !

We'll find a fraction that has the same number on top or bottom, but in different units, and we'll multiply our answer by this fraction.  It won't CHANGE our answer because we're only multiplying it by ' 1 '; but If we're clever about how we build the fraction, it can solve the problem of the units for us.

The fraction to use is . . .  (1 hour / 60 minutes) .

The top and the bottom are the same quantity, so the value of the fraction is ' 1 ', and we can multiply our answer by it without changing the answer. But watch what it does to our units:

Distance = (180 km · min / hr) · (1 hr / 60 min)

Distance = (180 · 1 / 60) (km · min · hr / hr · min)

(Do some canceling, and you get ...)

Distance = 3 km

Thank you.  Thank you very much.  Thank you.  I'll be here until Thursday.  don't forget to tip your waiter.

Answer 2

3 kilometers, it is just 5/60 or 1/12 multiplied by 36.