document.write( "Question 936925: a bus travels 10 kph faster than a truck. It travels 360 km in 3 h less time than the time required by the truck to travel the same distance. Find the rate of each. \n" ); document.write( "

Algebra.Com's Answer #570510 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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a bus travels 10 kph faster than a truck.
\n" ); document.write( " It travels 360 km in 3 h less time than the time required by the truck to travel the same distance.
\n" ); document.write( " Find the rate of each.
\n" ); document.write( ":
\n" ); document.write( "let s = the speed of the bus
\n" ); document.write( "then
\n" ); document.write( "(s-10) = the speed of the truck
\n" ); document.write( ":
\n" ); document.write( "Write a time equation, time = dist/speed
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\n" ); document.write( "Truck travel time - bus travel time = 3 hrs
\n" ); document.write( " $\"360%2F%28%28s-10%29%29\"$ - $\"360%2Fs\"$ = 3
\n" ); document.write( "multiply the equation by s(s-10)
\n" ); document.write( "s(s-10)* $\"360%2F%28%28s-10%29%29\"$ - s(s-10)* $\"360%2Fs\"$ = 3s(s-10)
\n" ); document.write( "cancel the denominators and you have
\n" ); document.write( "360s - 360(s-10) = 3s(s-10)
\n" ); document.write( "360s - 360s + 3600 = 3s^2 - 30s
\n" ); document.write( "Combine on the right to form a quadratic equation
\n" ); document.write( "0 = 3s^2 - 30s - 3600
\n" ); document.write( "simplify divide the 3
\n" ); document.write( "s^2 - 10s - 1200 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(s-40)(s+30) = 0
\n" ); document.write( "the positive solution
\n" ); document.write( "s = 40 km is the speed of the bus
\n" ); document.write( "You find speed of the truck \n" ); document.write( "

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