document.write( "Question 518430: A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 22 miles per hour. What is the amount of time that the cyclist travels before overtaking the runner?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #345221 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
A long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour.
\n" ); document.write( " Two hours later, a cyclist starts at the beginning of the trail and travels at a rate of 22 miles per hour.
\n" ); document.write( " What is the amount of time that the cyclist travels before overtaking the runner?
\n" ); document.write( ":
\n" ); document.write( "let t = travel time of the bike
\n" ); document.write( "then
\n" ); document.write( "(t+2) = running time of the runner
\n" ); document.write( ":
\n" ); document.write( "When the bike overtakes the runner, they will have traveled the same distance
\n" ); document.write( "Write a distance equation; dist = speed * time
\n" ); document.write( ":
\n" ); document.write( "6(t+2) = 22t
\n" ); document.write( "6t + 12 = 22t
\n" ); document.write( "12 = 22t - 6t
\n" ); document.write( "12 = 16t
\n" ); document.write( "t = \"12%2F16\"
\n" ); document.write( "t = .75 hrs, or 45 min for the bike to overtake the ground-pounder
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check by finding the actual dist of each, they should be equal
\n" ); document.write( "22(.75) = 16.5 mi
\n" ); document.write( "6(2.75) = 16.5 mi\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );