document.write( "Question 507308: A train travels 189 miles in 3 hours. It traveled 55 mph for some of the time and 65 mph for some of the time. How many miles did it travel at 55 mph and how many miles did it travel at 65 mph. Thank you \n" ); document.write( "

Algebra.Com's Answer #340418 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
A train travels 189 miles in 3 hours.
\n" ); document.write( " It traveled 55 mph for some of the time and 65 mph for some of the time.
\n" ); document.write( " How many miles did it travel at 55 mph and how many miles did it travel at 65 mph.
\n" ); document.write( ":
\n" ); document.write( "let d = miles traveled at 65 mph
\n" ); document.write( "then
\n" ); document.write( "(189-d) = miles traveled at 55 mph
\n" ); document.write( ":
\n" ); document.write( "Write a time equation: time = dist/speed
\n" ); document.write( ":
\n" ); document.write( "Time at 65 + time at 55 = 3 hrs
\n" ); document.write( " $\"d%2F65\"$ + $\"%28%28189-d%29%29%2F55\"$ = 3
\n" ); document.write( "multiply by 715 to clear the denominators, results:
\n" ); document.write( "11d + 13(189-d) = 715(3)
\n" ); document.write( "11d + 2457 - 13d = 2145
\n" ); document.write( "11d - 13d = 2145 - 2457
\n" ); document.write( "-2d = -312
\n" ); document.write( "d = +156 mi at 65 mph
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "You can check this by finding the actual time at each speed
\n" ); document.write( "156/65 = 2.4 hrs
\n" ); document.write( "(189-156)/55 = .6 hrs
\n" ); document.write( "----------------------
\n" ); document.write( "total time: 3 hrs
\n" ); document.write( " \n" ); document.write( "

\n" );