SOLUTION: judy frog hops up a 2/3rd of the ladder, slides down a 1/7th of the ladder from where she is at to the ground and then climbs up 2/5th of the remaining ladder distance to the top.

Algebra ->  Expressions -> SOLUTION: judy frog hops up a 2/3rd of the ladder, slides down a 1/7th of the ladder from where she is at to the ground and then climbs up 2/5th of the remaining ladder distance to the top.       Log On


   

Question 1141118: judy frog hops up a 2/3rd of the ladder, slides down a 1/7th of the ladder from where she is at to the ground and then climbs up 2/5th of the remaining ladder distance to the top. How far is judy off the ground?
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let the height of the ladder be x.

judy frog hops up a 2/3rd of the ladder...

She is now at a height equal to 2/3 of the ladder: (2/3)x

... slides down a 1/7th of the ladder from where she is at to the ground...

The distance she slides down is 1/7 of (2/3)x; the distance sheis now above the ground is 6/7 of (2/3)x, which is (12/21)x = (4/7)x

... and then climbs up 2/5th of the remaining ladder distance to the top.

She is at 4/7 the height of the ladder; the distance remaining to the top is 3/7 of the height of the ladder. She climbs 2/5 of that distance:

(2/5)*(3/7)x = (6/35)x

The distance she is now off the ground is (4/7)x + (6/35)x = (20/25)x + (6/35)x = (26/35)x.

ANSWER: She finishes 26/35 of the height of the ladder off the ground.