Question 1104182
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<pre>
Let T be the Tom' speed and S be the Sam' speed.

    (the same consistent units of speed are used).


Then from he condition,  

S = 2T         (1)   ("It takes Tom twice as long as Sam to drive from A to B.")
S + 2T = D     (2)    ("If they start driving towards each other at the same time, they will meet one hour later.")

where D is the distance between A and B.


If instead they started driving in the same direction (with Sam driving towards B), 

then T has head start D, the relative speed is S-T  and the time before Sam will catch up Tom is


time = {{{D/(S-T)}}} =          (replace D with S + 2T, according to (2) )

     = {{{(S + 2T)/(S-T)}}} =          (replace S with 2T, according to (1) )

     = {{{(2T + 2T)/(2T-T)}}} = {{{(4T)/T}}} = 4 hours.


<U>Answer</U>.  It will take 4 hours before Sam will catch up Tom.
</pre>

Solved.


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See these relevant lessons on Travel and Distance 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems.lesson>Travel and Distance problems</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Travel-and-Distance-problems-for-two-bodies-moving-toward-each-other.lesson>Travel and Distance problems for two bodies moving in opposite directions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Typical-catching-up-Travel-and-Distance-problems.lesson>Travel and Distance problems for two bodies moving in the same direction (catching up)</A>

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