A car is driving at 90

kilometers per hour. How far, in meters, does

it travel in three seconds? So to answer this question

we’ll first convert 90 kilometers per hour

into meters per second, then determine the distance

traveled in three seconds. To do this conversion

we’ll use unit fractions, so begin by writing 90 kilometers

per hour as a fraction, which would be 90 kilometers per one hour. And our goal here is to

convert this rate into a rate where we have meters per second. Let’s begin by converting

the kilometers to meters. We’ll do this using the conversion that one kilometer equals 1,000 meters. So we’re going to multiply

it by a unit fraction, and because we want

kilometers to simplify out, we’ll put kilometers in the denominator, and meters in the numerator. And again, the conversion

is that 1,000 meters equals one kilometer. Because these units are equal, this fraction is equal to one, but notice how the units of

kilometers now simplifies out, leaving us with meters. Now we still have to

convert hours to seconds, so we’ll first convert hours to minutes by multiplying by another unit fraction. We don’t want hours in our

answer, so we’ll have to have hours in the numerator and

minutes in the denominator. And the conversion is that

one hour equals 60 minutes, so we’ll have one hour over 60 minutes. Notice now the units of

hours simplifies out, and now we’re left to

convert minutes to seconds. So we multiply it by

another unit fraction. We want minutes to

simplify out, so we’ll have minutes in the numerator and

seconds in the denominator, and our conversion is that

one minute equals 60 seconds. Minutes simplifies out. Notice how now we have the correct units, so now I’ll multiply across the numerator, multiply across the denominator, and then divide to get the unit rate. So in the numerator we have 90 times 1,000 times one times one, that’s 90,000 meters. And in our denominator

we have one times one times 60 times 60

seconds, or 3,600 seconds. Again, we’ll now convert

this to a unit rate by performing this division. So 90,000 divided by 3,600 is equal to 25 which means that unit rate is 25 meters per one second, which can also be written

as 25 meters per second. But our goal here is to

find the distance traveled in three seconds, where

distance equals rate times time. So the distance traveled is

equal to 25 meters per second times the time of 3 seconds,

which gives us 75 meters. A lot of times when working

with a distance formula we leave the units off like we did here, and then just put the units in our answer. But I do want to show this

again leaving the units in. We could have written this

as the distance equals the rate of 25 meters per one second times a time of three seconds,

which can be written as three seconds over one. Notice how in this form the

units of seconds simplifies out leaving us with the same

result of 75 meters. So one thing nice about

leaving the units in is that we never have to

second-guess ourselves about what the unit should

be because the units work themselves out. I hope you found this explanation helpful.

you realise you can just divide km/h by 3.6 everytime and get m/s