document.write( "Question 1161710: Antonio enjoys mountain biking. He has found that the maximum gradient which he can cycle up is 0.3 and the maximum gradient he can safely descend is 0.5. Antonio's map has a scale of 2cm to 1km with contours every 25m.
\n" ); document.write( "What is the maximum distance between the contours (lines on a map showing the height of land) on his map that allows him to go...
\n" ); document.write( "a) Up-hill?
\n" ); document.write( "b) Down-hill? \n" ); document.write( "

Algebra.Com's Answer #785357 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
A distance $\"x\"$ on the map (in cm) translates into an actual horizontal distance (in m) of
\n" ); document.write( " $\"x%2A%281km%2F%222+cm%22%29%2A%281000m%2F%221+km%22%29=500x\"$
\n" ); document.write( "Antonio can go up from one contour line on the map to the next
\n" ); document.write( "over a path with a distance $\"x\"$ if
\n" ); document.write( " $\"25%2F500x%3C=0.3\"$ --> $\"x%3E=25%2F%28500%2A0.3%29\"$ $\"cm\"$ --> $\"highlight%28x%3E=0.17cm%29\"$ (1.7mm).
\n" ); document.write( "(I rounded that result because I assume Antonio cannot see the difference between 1.7mm and 1.66666...mm).
\n" ); document.write( "if Antonio wants to follow an uphill path with a distance between contour lines of 0.2cm (2mm) he will be going up $\"25m\"$ , over a horizontal distance of
\n" ); document.write( " $\"0.2cm%2A%281km%2F%222+cm%22%29%2A%281000m%2F%221+km%22%29=100m\"$ .
\n" ); document.write( "That corresponds to a gradient of $\"25m%2F100m=0.25\"$ ,
\n" ); document.write( "Antonio can cycle up that path.
\n" ); document.write( "
\n" ); document.write( "When going downhill the $\"x\"$ (in cm) should satisfy
\n" ); document.write( " $\"25%2F500x%3C=0.5\"$ --> $\"x%3E=25%2F%28500%2A0.5%29\"$ $\"cm\"$ --> $\"highlight%28x%3E=0.10cm%29\"$ (1.0mm). \n" ); document.write( "

\n" );