document.write( "Question 553716: hi i need help in solvinf this worded question which has confused me in what i should do. I need help on the following question:
\n" ); document.write( "a car travels x km at 50 km/h and y km at 60 km/h. The total time taken is 5 hours. if the average speed for the journey is 56km/h, what are x and y? \r
\n" ); document.write( "\n" ); document.write( "i have already found the total distance of the journey which is 280km. how do i find x and y. thanks \n" ); document.write( "
Algebra.Com's Answer #361004 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
rate * time = distance
\n" ); document.write( "for the total distance we get 56*5 = d which becomes 280 = d
\n" ); document.write( "total distance = 280 km.
\n" ); document.write( "you got that part right.
\n" ); document.write( "x equals the distance traveled at 50 kmph and y equals the distance traveled at 60 kmph.
\n" ); document.write( "we get:
\n" ); document.write( "x + y = 280
\n" ); document.write( "we also know from the formula of rate * time = distance that:
\n" ); document.write( "50T1 = x
\n" ); document.write( "60T2 = y
\n" ); document.write( "where T1 and T2 are the times to go distance x and distance y.
\n" ); document.write( "we know tht T1+ T2 = 5 hours.
\n" ); document.write( "this means that:
\n" ); document.write( "T1 + T2 = 5 hours
\n" ); document.write( "from the equation of 50T1 = x, we solve for T1 to get T1 = x/50
\n" ); document.write( "from the equation of 60T2 = y, we solve for T2 to get T2 = y/60
\n" ); document.write( "we substitute for T1 and T2 in the equaqtion of T1 + T2 = 5 hours to get:
\n" ); document.write( "x/50 + y/60 = 5
\n" ); document.write( "we have 2 equations that we need to solve simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "x + y = 280
\n" ); document.write( "x/50 + y/60 = 5
\n" ); document.write( "multiply both sides of the second equation by 60 to get:
\n" ); document.write( "60x/50 + 60y/60 = 5*60
\n" ); document.write( "this simplifies to:
\n" ); document.write( "(6/5)x + y = 300
\n" ); document.write( "our 2 equations are now:
\n" ); document.write( "x + y = 280
\n" ); document.write( "(6/5)x + y = 300
\n" ); document.write( "multiply the first equation by -1 and then add the 2 equations together to get:
\n" ); document.write( "(1/5)x = 20
\n" ); document.write( "divide both sides of this equation by (1/5) to get:
\n" ); document.write( "x = 100
\n" ); document.write( "if x = 100, and x + y = 280, then y = 180
\n" ); document.write( "we have:
\n" ); document.write( "x = 100
\n" ); document.write( "y = 180
\n" ); document.write( "the car travels for 100 miles at 50 miles per hours and 180 miles at 60 miles per hour to gain a total distance of 280 miles.
\n" ); document.write( "x + y becomes 100 + 180 which equals 280.
\n" ); document.write( "the car travels 100 miles at 50 miles per hour for 2 hours.
\n" ); document.write( "the car travels 180 miles at 60 miles per hour for 3 hours.
\n" ); document.write( "total time is 5 hours.
\n" ); document.write( "x/50 + y/60 = 5
\n" ); document.write( "100/50 + 180/60 = 5
\n" ); document.write( "figures check out so the answer is good.
\n" ); document.write( "x = 100
\n" ); document.write( "y = 180
\n" ); document.write( "time to travel 100 miles at 50 miles per hour is 2 hours.
\n" ); document.write( "time to travel 180 miles at 60 miles per hour is 3 hours.
\n" ); document.write( "total distance is 280
\n" ); document.write( "total time is 5 hours\r
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