document.write( "Question 932993: The distance between towns A and B is 39km. A cyclist and a bus moved from A to B at constant speeds. A bus left A 15 minutes after a cyclist did and caught up with the cyclist in 10 minutes. After reaching B, the bus immediately turned around, and 30 minutes after the first meeting met the cyclist the second time. Find the speeds of the car and the cyclist. \n" ); document.write( "
Algebra.Com's Answer #566685 by ankor@dixie-net.com(22740)\"\" \"About 
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The distance between towns A and B is 39km.
\n" ); document.write( "A cyclist and a bus moved from A to B at constant speeds.
\n" ); document.write( "A bus left A 15 minutes after a cyclist did and caught up with the cyclist in 10 minutes.
\n" ); document.write( "After reaching B, the bus immediately turned around, and 30 minutes after the first meeting met the cyclist the second time.
\n" ); document.write( "Find the speeds of the car and the cyclist.
\n" ); document.write( ":
\n" ); document.write( "A----x------*1st----------------*2nd------y------B
\n" ); document.write( ":
\n" ); document.write( "let x = distance from A to the 1st meeting point
\n" ); document.write( "Travel time of the cycle to x: 15 + 10 = 25 min
\n" ); document.write( "travel time of the bus to x: 10 min
\n" ); document.write( "therefore
\n" ); document.write( "\"x%2F25\" = speed of the cyle
\n" ); document.write( "\"x%2F10\" = speed of the bus
\n" ); document.write( ":
\n" ); document.write( "let y = distance from B to the 2nd meeting point
\n" ); document.write( "The total travel time of cycle: 25 + 30 = 55 min
\n" ); document.write( "The total travel time of the bus: 10 + 30 = 40 min
\n" ); document.write( "\"%2839-y%29%2F55\" = speed of the cycle
\n" ); document.write( "\"%2839%2By%29%2F40\" = speed of the bus
\n" ); document.write( ":
\n" ); document.write( "Speed of cycle equation
\n" ); document.write( "\"x%2F25\" = \"%2839-y%29%2F55\"
\n" ); document.write( "cross multiply
\n" ); document.write( "55x = 25(39-y)
\n" ); document.write( "55x = 975 - 25y
\n" ); document.write( "55x + 25y = 975
\n" ); document.write( "simplify divide by 5
\n" ); document.write( "11x + 5y = 195
\n" ); document.write( "Speed of bus equation
\n" ); document.write( "\"x%2F10\" = \"%2839%2By%29%2F40\"
\n" ); document.write( "Cross multiply
\n" ); document.write( "40x = 10(39+y)
\n" ); document.write( "40x = 390 + 10y
\n" ); document.write( "40x - 10y = 390
\n" ); document.write( "simplify divide by 2
\n" ); document.write( "20x - 5y = 195
\n" ); document.write( ":
\n" ); document.write( "Use elimination on these two equations
\n" ); document.write( "11x + 5y = 195
\n" ); document.write( "20x - 5y = 195
\n" ); document.write( "----------------adding eliminates y find x
\n" ); document.write( "31x = 390
\n" ); document.write( "x = 390/31
\n" ); document.write( "x = 12.58 km from A to the 1st meeting place
\n" ); document.write( ":
\n" ); document.write( "Find the cycle speed in km/hr
\n" ); document.write( "\"12.58%2F%2825%2F60%29\" = 30.2 km/hr speed of the cycle
\n" ); document.write( "find the bus speed
\n" ); document.write( "\"12.58%2F%2810%2F60%29\" = 75.5 km/hr speed of the bus
\n" ); document.write( ":
\n" ); document.write( ";
\n" ); document.write( "To check this find y using 11x + 5y = 195
\n" ); document.write( "11(12.58) + 5y = 195
\n" ); document.write( "5y = 195 - 138.4
\n" ); document.write( "5y = 56.6
\n" ); document.write( "y = 56.6/5
\n" ); document.write( "y = 11.3 km dist from B to the 2nd meeting point
\n" ); document.write( "We know the bus traveled 11.3 + 39 = 50.3 km in 40 min
\n" ); document.write( "\"50.3%2F%2840%2F60%29\" = 75.45, agrees with our previous calc for the bus speed
\n" ); document.write( "You can check it by finding the cycle speed to the 2nd meeting (39-11.3) \n" ); document.write( "
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