document.write( "Question 401313: Alex is a faster runner than Bob. Alex runs 3 yards every second. Bob runs 2.5 yards every second. Alex gives Bob a 30 yard head start in a race, and reaches the finish line exactly 2 seconds before Bob. How many yards did Alex run? \n" ); document.write( "

Algebra.Com's Answer #283987 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Alex is a faster runner than Bob. Alex runs 3 yards every second.
\n" ); document.write( " Bob runs 2.5 yards every second.
\n" ); document.write( " Alex gives Bob a 30 yard head start in a race, and reaches the finish line exactly 2 seconds before Bob.
\n" ); document.write( "How many yards did Alex run?
\n" ); document.write( ":
\n" ); document.write( "Let d = distance run by Alex
\n" ); document.write( "then
\n" ); document.write( "(d-30) = distance run by Bob (after Alex starts)
\n" ); document.write( ":
\n" ); document.write( "Write a time equation, Time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "Bob's time - Alex's time = 2 sec
\n" ); document.write( " $\"%28%28d-30%29%29%2F2.5\"$ - $\"d%2F3\"$ = 2 sec
\n" ); document.write( "Multiply eq by 15
\n" ); document.write( "15* $\"%28%28d-30%29%29%2F2.5\"$ - 15* $\"d%2F3\"$ = 15(2)
\n" ); document.write( "Cancel denominators, results:
\n" ); document.write( "6(d-30) - 5d = 30
\n" ); document.write( "6d - 180 - 5d = 30
\n" ); document.write( "6d - 5d = 30 + 180
\n" ); document.write( "d = 210 yds run by Alex
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check by finding the actual time of each; (Bob runs 210 - 30 = 180 yds)
\n" ); document.write( "180/2.5 = 72 seconds
\n" ); document.write( "210/3.0 = 70 seconds
\n" ); document.write( "---------------------
\n" ); document.write( "difference 2 seconds
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