document.write( "Question 825712: Two cars are leaving at the same time from two diffirent provinces which are 150 km apart. If car A travels at 5 kph faster than car B, find their rates if they meet after two hours. \n" ); document.write( "
Algebra.Com's Answer #497635 by math-vortex(648) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Two cars are leaving at the same time from two diffirent provinces which are 150 km apart. If \r\n" );
document.write( "car A travels at 5 kph faster than car B, find their rates if they meet after two hours.\r\n" );
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document.write( "A SOLUTION:\r\n" );
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document.write( "We need to use the big idea that [Rate] * [Time] = [Distance].\r\n" );
document.write( "We also assume that the cars are traveling straight towards each other. Furthermore, each car \r\n" );
document.write( "travels at a constant speed.\r\n" );
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document.write( "We want to find the rate of each car.\r\n" );
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document.write( "Define variables and expressions:\r\n" );
document.write( "Let r be the rate of the car A (in km/hr). \r\n" );
document.write( "Then the rate of car B will be r-5 because Car A is driving faster.\r\n" );
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document.write( "We know the cars are 150 km apart at the start.\r\n" );
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document.write( "We know that the cars will meet somewhere in the middle. It won't be exactly in the middle, \r\n" );
document.write( "though, because car A is driving faster and can cover more territory in 2 hours. \r\n" );
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document.write( "We can say that their combined distance traveled is 150 km. Do you see why that is?\r\n" );
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document.write( "We need to write an expression for the distance each car travels and then write an equation \r\n" );
document.write( "showing the sum of the distance to be 150 km.\r\n" );
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document.write( "Car A:\r\n" );
document.write( "Car A travels at a rate of r km/hr. It travels for 2 hours until the two drivers meet.\r\n" );
document.write( "[Rate] * [Time] = [Distance] so an expression for car B's distance is r*2, or 2r.\r\n" );
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document.write( "Car B:\r\n" );
document.write( "[Rate} * [Time] = [Distance] so an expression for car B's distance is (r-5)*2, or 2(r-5).\r\n" );
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document.write( "Now our equation is [Car A's distance] + [car B's distance] = [150 km]\r\n" );
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document.write( "Substitute each expression into the equation and we have\r\n" );
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document.write( "Simplify and solve for r.\r\n" );
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document.write( "In the context of this problem, r=40 means that car A's rate is 40 km/hr. Since car B\r\n" );
document.write( "is traveling 5 km/hr slower than car A, car B's rate is 40-5=35 km/hr.\r\n" );
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document.write( "Let's check our work against the words in the original problem.\r\n" );
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document.write( "\"Car A is traveling 5 kph faster than Car B.\" We see that 40 kph is 5 kph faster. CHECK!\r\n" );
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document.write( "\"The cars are...150 km apart…they meet after two hours.\" \r\n" );
document.write( "In 2 hours, Car A travels 80 km (40 km for each hour.)\r\n" );
document.write( "In 2 hours, Car B travels 70 km (35 km for each hour.)\r\n" );
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document.write( "They started 150 km apart and headed toward each other. When they met after 2 hours, they \r\n" );
document.write( "had covered 80+70=150 km. CHECK!\r\n" );
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document.write( "Hope this helps!\r\n" );
document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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