document.write( "Question 363327: A semi- truck travels 360 miles through flatline in the same amount of time it travels 180 miles through the mountains. The rate of the truck is 25 miles per hour slower in the mountains than in the flatland. Find both the flatline rate and mountain rate. \n" ); document.write( "

Algebra.Com's Answer #259189 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A semi-truck travels 360 miles through flatland in the same amount of time
\n" ); document.write( " it travels 180 miles through the mountains.
\n" ); document.write( " The rate of the truck is 25 miles per hour slower in the mountains than in the flatland.
\n" ); document.write( " Find both the flatland rate and mountain rate.
\n" ); document.write( ":
\n" ); document.write( "Let r = the slow rate through the mountains
\n" ); document.write( "then
\n" ); document.write( "(r+25) = the faster rate through flat areas
\n" ); document.write( ":
\n" ); document.write( "Write a time equation; time = dist/rate
\n" ); document.write( ":
\n" ); document.write( "Flat time = Mountain time
\n" ); document.write( " $\"360%2F%28%28r%2B25%29%29\"$ = $\"180%2Fr\"$
\n" ); document.write( "Cross multiply
\n" ); document.write( "360r = 180(r+25)
\n" ); document.write( "360r = 180r + 4500
\n" ); document.write( "360r - 180r = 4500
\n" ); document.write( "180r = 4500
\n" ); document.write( "r = 4500/180
\n" ); document.write( "r = 25 mph through the mountains
\n" ); document.write( "then
\n" ); document.write( "25 + 25 = 50 mph on the flat
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check solution by finding the actual times, they should be equal
\n" ); document.write( "360/50 = 7.2 hrs
\n" ); document.write( "180/25 = 7.2 hrs also \n" ); document.write( "

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