document.write( "Question 1197435: plese help me in my homework thankyousomuch!!
\n" ); document.write( "car at a certain speed travels 120km during the first part. On the second part, it reduces its speed by 10kph when it travels 100km.find the speed on each part of the trip in the trip lasted for 4hours \n" ); document.write( "

Algebra.Com's Answer #830710 by math_tutor2020(3816) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

	Distance (km)	Rate (kph)	Time (hr)
1st Part	120	x	120/x
2nd Part	100	x-10	100/(x-10)
Total	220		4

\n" ); document.write( "Notes:
\n" ); document.write( "distance = rate*time
\n" ); document.write( "time = distance/rate\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The two time durations of 120/x and 100/(x-10) must add to the 4 hour total time.
\n" ); document.write( "We'll use this fact to set up our equation and solve for x.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "120/x + 100/(x-10) = 4
\n" ); document.write( "x(x-10)( 120/x + 100/(x-10) ) = x(x-10)*4
\n" ); document.write( "120(x-10) + 100x = 4x^2-40x
\n" ); document.write( "120x-1200 + 100x = 4x^2-40x
\n" ); document.write( "0 = 4x^2-40x+1200-220x
\n" ); document.write( "4x^2-260x+1200 = 0
\n" ); document.write( "In the second step, I multiplied both sides by x(x-10) to clear out the fractions.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We'll turn to the quadratic formula to solve for x.
\n" ); document.write( "Use a = 4, b = -260, c = 1200
\n" ); document.write( " $\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-%28-260%29%2B-sqrt%28%28-260%29%5E2-4%284%29%281200%29%29%29%2F%282%284%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28260%2B-sqrt%2867600-19200%29%29%2F%288%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28260%2B-sqrt%2848400%29%29%2F%288%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28260%2B-++220%29%2F%288%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28260%2B220%29%2F%288%29\"$ or $\"x+=+%28260-220%29%2F%288%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28480%29%2F%288%29\"$ or $\"x+=+%2840%29%2F%288%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+60\"$ or $\"x+=+5\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The solution x = 5 isn't possible since x-10 = 5-10 = -5. It doesn't make sense to have a negative speed.
\n" ); document.write( "We'll ignore it and go with x = 60 as the only possible value of x.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If x = 60, then x-10 = 60-10 = 50\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "Traveling 120 km at a speed of 60 kph means you take 120/60 = 2 hours.
\n" ); document.write( "Traveling 100 km at a speed of 50 kph means you take 100/50 = 2 hours.
\n" ); document.write( "That's a total of 2+2 = 4 hours to confirm our answers.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Answers:
\n" ); document.write( "Speed on the 1st part: 60 kph
\n" ); document.write( "Speed on the 2nd part: 50 kph
\n" ); document.write( " \n" ); document.write( "

\n" );