Question 158128
A woman driving a car 14 ft long is passing a truck 30 ft long. The truck is traveling at 50 mi/h. How fast must the woman drive her car so that she can pass the truck completely in 6 s, from the position shown in figure (A) to the position shown in figure (B)?
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She would really have to be flying to pass that truck in
only 6 seconds.

First we must change 50 mi/h to ft/s.

{{{(50mi)/(1h)}}}

replace {{{mi}}} by {{{5280ft}}}
replace {{{1h}}} by {{{60min}}}

{{{(50(5280ft))/(60min)}}}

replace {{{min}}} by {{{60s}}}

{{{(50(5280ft))/(60(60s))}}}

{{{264000ft/(3600s)}}}

{{{(220ft)/(3s)}}}

So in 6 seconds, using {{{d=rt}}},
the truck travels

{{{d=rt=((220ft)/(3s))(6s)= 440ft}}}

We start with the front bumper of the car even
with the tailgate of the truck.

So in that 6 seconds, the front bumper of the 
car must travel:

1. the 440 feet which the truck travels in 6 seconds.
2. the 30 feet from the tailgate of the
   truck to the front bumper of the truck.
3. the 14 feet to get the back bumper of
   the car even with the front bumper of the
   truck.

That's a total of {{{440+30+14=484}}}feet, which she
must travel in 6 second.  

Now we find her rate using {{{r=d/t}}}

{{{r=(484ft)/(6s)}}}
{{{r=(484ft)/(6s)}}}
{{{r=(242ft)/(3s)}}}
{{{r=(242ft)/(3s)}}}

Now we must get that to {{{mi/h}}}:

Multiply by {{{(1mi)/(5280ft)}}}

{{{r=(242ft)/(3s)}}}×{{{(1mi)/(5280ft)}}}

Multiply by {{{60s/1min}}}

{{{r=(242ft)/(3s)}}}×{{{(1mi)/(5280ft)}}}×{{{60s/1min}}}

Multiply by {{{(60min)/(1hr)}}}

{{{r=(242ft)/(3s)}}}×{{{(1mi)/(5280ft)}}}×{{{60s/1min}}}×{{{(60min)/(1hr)}}}

Cancel the {{{ft}}}, the {{{s}}}, and the {{{min}}}:

{{{r=(242cross(ft))/(3cross(s))}}}×{{{(1mi)/(5280cross(ft))}}}×{{{60cross(s)/1cross(min)}}}×{{{(60cross(min))/(1hr)}}}

{{{r=165}}}{{{mi/h}}}

That's fast!!!  I don't she'll do it, do you?

Edwin</pre>