Apole vaulter uses a 15 foot long pole. she grips the pole so that the segment below her left hand is twice the length of the segment above her left hand. her right hand grips thee pole 1.5 feet above her left hand. how far up the pole is her right hand

The pole is 3.5 foot above the right hand.
To answer this question first you need to determine the left hand height/position. The left hand divides the pole segment into 2:1 ratio. If the pole if 15 foot long, then the equation will be:
2/(2+1)x 15 foot= 10 foot.

The left hand is located 10 foot from the ground and the right hand is 1.5 foot above it. Then the right hand position from the ground is:
10 foot+ 1.5 foot= 11.5 foot

Since the right hand is 11.5 foot from ground and the pole is 15 foot long, then the equation will be:
15 foot- 11.5 foot= 3.5 foot.