document.write( "Question 1023795: 1. One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 8 hours. How long will it take the pipe to fill the pool if the drain is left open?\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2. Hannah can paint a room in 8 hours. Destiny can paint the same room in 6 hours. How long does it take for both Hannah and Destiny to paint the room it they are working together.\r
\n" ); document.write( "\n" ); document.write( "3.A plane can fly 360 miles in the same time as it takes a car to go 90 miles. If the car travels 90 mph slower than the plane, find the speed of the plane.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #639292 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
1. One inlet pipe can fill an empty pool in 6 hours, and a
\n" ); document.write( "drain can empty the pool in 8 hours. How long will it take
\n" ); document.write( "the pipe to fill the pool if the drain is left open?
\n" ); document.write( "
\r\n" );
document.write( "               Part of pool   =   Rate in   times  Time in\r\n" );
document.write( "                filled            pool/hr           hours   \r\n" );
document.write( "Inlet pipe         1                1/6               6\r\n" );
document.write( "Outlet pipe       -1               -1/8               8\r\n" );
document.write( "Both open          1                1/T               T\r\n" );
document.write( "\r\n" );
document.write( "Rate of Inlet + Rate of outlet = Together rate\r\n" );
document.write( "       1/6    +   (-1/8)       =  1/T\r\n" );
document.write( "\r\n" );
document.write( "Multiply by 24T\r\n" );
document.write( "   \r\n" );
document.write( "       4T    -       3T        =  24\r\n" );
document.write( "                      T        =  24\r\n" );
document.write( "\r\n" );
document.write( "It'll take 24 hours. \r\n" );
document.write( "

\n" ); document.write( "2. Hannah can paint a room in 8 hours. Destiny can paint
\n" ); document.write( "the same room in 6 hours. How long does it take for both
\n" ); document.write( "Hannah and Destiny to paint the room it they are working
\n" ); document.write( "together?
\n" ); document.write( "
\r\n" );
document.write( "               Part of room       Rate in         Time in\r\n" );
document.write( "                 painted          room/hr           hours   \r\n" );
document.write( "Hannah             1                1/6               6\r\n" );
document.write( "Destiny            1                1/8               8\r\n" );
document.write( "Both painting      1                1/T               T\r\n" );
document.write( "\r\n" );
document.write( "Rate of Hannah + Rate of Destiny = Together rate\r\n" );
document.write( "       1/6    +        1/8       =  1/T\r\n" );
document.write( "\r\n" );
document.write( "Multiply by 24T\r\n" );
document.write( "   \r\n" );
document.write( "       4T    +       3T        =  24\r\n" );
document.write( "                     7T        =  24\r\n" );
document.write( "                      T        =  24/7 or 3 3/7 hours.  \r\n" );
document.write( "It'll take 3 3/7 hours. \r\n" );
document.write( "

\n" ); document.write( "3.A plane can fly 360 miles in the same time as it
\n" ); document.write( "takes a car to go 90 miles. If the car travels
\n" ); document.write( "90 mph slower than the plane, find the speed of
\n" ); document.write( "the plane.
\n" ); document.write( "
\r\n" );
document.write( "          Distance   =    Rate in       Time in\r\n" );
document.write( "          traveled       miles/hour     hours = dist./rate   \r\n" );
document.write( "Plane        360              x           360/x\r\n" );
document.write( "Car           90             x-90        90/(x-90)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          Plane's time = Car's time.\r\n" );
document.write( "\r\n" );
document.write( "                 360/x = 90/(x-90)\r\n" );
document.write( "\r\n" );
document.write( "Cross multiply\r\n" );
document.write( "\r\n" );
document.write( "             360(x-90) = 90x\r\n" );
document.write( "            360x-32400 = 90x\r\n" );
document.write( "                  270x = 32400\r\n" );
document.write( "                     x = 32400/270\r\n" );
document.write( "                     x = 120 miles/hour\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );