Constant of the variation?

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1 Answer
Feb 10, 2018

1 hour 42 minutes at 60 mph

Very detailed explanation given. With practice you will be able to do this type of question in just a few lines.

Explanation:

Let time be #t# in hours
Let distance be #d# in miles
Let speed (velocity) be #v# in miles per hour

velocity #->v="miles per hour "->("miles")/("hour")->m/h#

distance = velocity * time

Initial given condition:

#color(brown)("Unites of measurement in green. Values in red")#

#color(blue)("Setting up initial conditions")#

#color(green)(color(red)(d)m=color(red)(v) m/hxxcolor(red)(t)h)#

#color(green)(color(red)(d)m=color(red)(54) m/hxxcolor(red)(3)h)#

#color(green)(color(red)(d)m=color(red)(54xx3)color(white)( "d") m/cancel(h)xxcancel(h))#

#color(green)(color(red)(d)m=color(red)(162)m#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Time taken for 60 mph")#

#color(green)(color(red)(d)m=color(red)(v) m/hxxcolor(red)(t)h)#

#color(green)(color(red)(162)m = color(red)(60) m/h xx color(red)(t)h)#

We need #color(red)(t)# to be on its own on one side of the = and everything else on the other side

Divide both sides by #60 m/h# which is the same as multiplying both sides by # 1/60h/m # ( all of it turned up the other way)

#color(green)(color(red)(162)m color(red)(xx1/60)h/mcolor(white)( "ddd") =color(white)( "ddd") color(red)(60) m/h color(red)(xx1/60)h/mxx color(red)(t)h)#

Dealing with just the units of measurement we have:
#color(green)(color(red)(162)cancel(m) color(red)(xx1/60)h/cancel(m)color(white)( "ddd") =color(white)( "ddd") color(red)(60) cancel(m)/cancel(h) color(red)(xx1/60)cancel(h)/cancel(m)xx color(red)(t)h)#

Now we just have hours #color(green)(h)# on both sides
Dealing with just the numbers we have:

#color(red)(162/60color(green)(h)=cancel(60)^1/cancel(60)^1xxtcolor(green)(h)#

#color(red)( 1 42/60color(green)( h)=tcolor(green)(h))#

Time #color(green)( color(red)(t)= color(red)(1)" hour "color(red)(42)" minutes")#