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tina hiked 15 km up a mountain trail.
\n" ); document.write( " Her return trip along the same trail took 30 minutes less because she was able to increase her speed by 1km/hour.
\n" ); document.write( "how long did it take her to climb up and down the mountain?
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\n" ); document.write( "Change 30 min to .5 hrs
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\n" ); document.write( "Find the hiking rate first, then find the time:
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\n" ); document.write( "Let r = T's rate up the mt
\n" ); document.write( "then
\n" ); document.write( "(r+1) = time down the mt
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\n" ); document.write( "Write a time equation; time = dist/speed
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\n" ); document.write( "Time up the mt - time down the mt = .5 hrs
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\n" ); document.write( "multiply equation by r(r+1), results
\n" ); document.write( "15(r+1) - 15r = .5r(r+1)
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\n" ); document.write( "15r + 15 - 15r = .5r^2 + .5r
\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( ".5r^2 + .5r - 15 = 0
\n" ); document.write( "Multiply by 2, get rid of the decimals
\n" ); document.write( "r^2 + r - 30 = 0
\n" ); document.write( "Factor
\n" ); document.write( "(r+6)(r-5) = 0
\n" ); document.write( "the positive solution is what we want here
\n" ); document.write( "r = 5 km/hr hiking rate up the mt
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\n" ); document.write( "Find the time up:
\n" ); document.write( "15/5 = 3 hrs
\n" ); document.write( "find the time down
\n" ); document.write( "15/6 = 2.5 hrs, (a difference of 30 min)
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