document.write( "Question 668771: A truck left a depot at noon traveling an average of 40 kilometers per hour. How far from the depot and at what time will it overtake another truck, which left the same depot 2 hours earlier and was traveling 30 kilometers per hour? \n" ); document.write( "

Algebra.Com's Answer #415835 by josmiceli(19441) $\"\"$ $\"About$

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The truck that left earlier had a head start of
\n" ); document.write( " $\"+30%2A2+=+60+\"$ km
\n" ); document.write( "Let $\"+d+\"$ = distance the truck that left at noon went
\n" ); document.write( "until it overtook the earlier truck
\n" ); document.write( "Let $\"+t+\"$ = time to overtake earlier truck
\n" ); document.write( "Equation for truck that left at noon:
\n" ); document.write( "(1) $\"+d+=+40t+\"$
\n" ); document.write( "Equation for truck that left 2 hrs earlier:
\n" ); document.write( "(2) $\"+d+-+60+=+30t+\"$
\n" ); document.write( "------------------
\n" ); document.write( "(2) $\"+d+=+60+%2B+30t+\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"+40t+=+60+%2B+30t+\"$
\n" ); document.write( " $\"+10t+=+60+\"$
\n" ); document.write( " $\"+t+=+6+\"$
\n" ); document.write( "At 6 PM the 2nd truck overtakes the 1st
\n" ); document.write( " $\"+d+=+40t+\"$
\n" ); document.write( " $\"+d+=+40%2A6+\"$
\n" ); document.write( " $\"+d+=+240+\"$
\n" ); document.write( "the 2nd truck overtakes the 1st 240 km from depot
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+d+-+60+=+30t+\"$
\n" ); document.write( "(2) $\"+d+-+60+=+30%2A6+\"$
\n" ); document.write( "(2) $\"+d+=+60+%2B+180+\"$
\n" ); document.write( "(2) $\"+d+=+240+\"$ km
\n" ); document.write( "OK\r
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