document.write( "Question 242547: Jake cycled 20 km to the beach. He returned cycling 1 km/h faster. The total time for the round trip was 9 h. Find his rate for each part of the trip. \n" ); document.write( "

Algebra.Com's Answer #177942 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Jake cycled 20 km to the beach. He returned cycling 1 km/h faster.
\n" ); document.write( " The total time for the round trip was 9 h.
\n" ); document.write( " Find his rate for each part of the trip.
\n" ); document.write( ":
\n" ); document.write( "Let r = rate to the beach
\n" ); document.write( "then
\n" ); document.write( "(r+1) = rate from the beach
\n" ); document.write( ":
\n" ); document.write( "Write a time equation: time = dist/rate
\n" ); document.write( ":
\n" ); document.write( "To time + from time = 9 hrs
\n" ); document.write( " $\"20%2Fr\"$ + $\"20%2F%28r%2B1%29\"$ = 9
\n" ); document.write( "Multiply by r(r+1), results:
\n" ); document.write( "20(r+1) + 20r = 9r(r+1)
\n" ); document.write( ":
\n" ); document.write( "20r + 20 + 20r = 9r^2 + 9r
\n" ); document.write( ":
\n" ); document.write( "40r + 20 = 9r^2 + 9r
\n" ); document.write( ":
\n" ); document.write( "0 = 9r^2 + 9r - 40r - 20
\n" ); document.write( ":
\n" ); document.write( "9r^2 - 31r - 20 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(9r+5)(r-4) = 0
\n" ); document.write( "positive solution
\n" ); document.write( "r = 4 km/hr to the beach
\n" ); document.write( "then
\n" ); document.write( "5 km/hr from the beach
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution
\n" ); document.write( "20/4 + 20/5 = 9 \n" ); document.write( "

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