document.write( "Question 768531: an automobile travels at a uniform rate. If the rate were 5 kilometers per hour faster, the distance traveled in 9 hours would be 50 kilometers more than the distance traveled in 11 hours at the rate of 5 kilometers per hour less than the actual rate. Find the actual rate. \n" ); document.write( "

Algebra.Com's Answer #468372 by ramkikk66(644) $\"\"$ $\"About$

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document.write( "An automobile travels at a uniform rate. If the rate were 5 kilometers per hour faster, the distance traveled in 9 hours would be 50 kilometers more than the distance traveled in 11 hours at the rate of 5 kilometers per hour less than the actual rate. Find the actual rate.
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document.write( "Ans:
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document.write( "Let the actual rate be x kph
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document.write( "If the rate is 5 kph faster, it is (x+5) kph
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document.write( "At the faster rate, distance travelled in 9 hours = 9*(x+5) = 9*x + 45
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document.write( "If the rate is 5 kph slower, it is (x-5) kph
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document.write( "At the slower rate, distance travelled in 11 hours = 11*(x-5) = 11*x - 55
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document.write( "It is given that the first distance (faster rate) is 50 km more than the second (slower rate).
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document.write( "We get the equation
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document.write( "Simplifying
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document.write( " or 
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document.write( "Actual speed =  kmph
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document.write( "Check for correctness:
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document.write( "At 5 kph higher speed, i.e. 30 kph, distance in 9 hours = 9 * 30 = 270
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document.write( "At 5 kph slower speed, i.e. 20 kph, distance in 11 hours = 11 * 20 = 220
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document.write( "270 - 220 = 50. So the answer is correct.
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