SOLUTION: three hours of videotape contains two movies with lengths that are in the ration 5:3 what is the difference in the lengths of the movie in minutes
Question 1142562: three hours of videotape contains two movies with lengths that are in the ration 5:3 what is the difference in the lengths of the movie in minutes Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! total is 3 hours.
x = time for first video
y = time for second video
x + y = 3 is your first equation.
videos are in ratio of 5:3.
ratio is therefore x/y = 5/3
solve for x to get x = 5/3 * y
that's your second equation.
in the first equation, replace x with 5/3 * y to get:
5/3 * y + y = 3
combine like terms to get 8/3 * y = 3
multiply both sides of the equation by 3/8.
solve for y to get y = 3 * 3/8 = 9/8.
x + y = 3 becomes x + 9/8 = 3
subtract 9/8 from both sides of the equation to get:
x = 3 - 9/8 = 24/8 - 9/8 = 15/8.
you have x = 15/8 and you have y = 9/8
15/8 + 9/8 = 24/8 = 3
(15/8) / (9/8) = (15/8) * (8/9) = 15/9 = 5/3.
the sum is good and the ratio is good.
first movie takes 15/8 hours and second movie takes 9/8 hours.
you were asked for the difference.
the difference is 15/8 - 9/8 = 6/8 = 3/4 of an hour.
Total video-tape time : 3 hours, or 180 minutes
Length of longer segment:
Length of shorter segment:
Difference in segment-lengths:
That's it. Nothing COMPLEX in this!!