A pole-vaulter uses a 15-foot-long pile. 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 the pole 1.5 above her left hand. How far up the pole is her right hand?

Let x + 1.5 be length of segment above left hand

Let 2x be length of segment below left hand

15 = x + 1.5 + 2x

15 = 3x + 1.5

15 - 1.5 = 3x

13.5 = 3x

13.5/3 = 3x/3

4.5 = x

x = 4.5

This is the length above the left hand.

2x must be then 4.5*2 = 9 foot

This is the length below the left hand.

Checking

4.5 + 9 + 1.5 = 15 foot

Adding length below left hand & length of left hand to right hand:

9 + 1.5 = 10.5

The right hand is hence 10.5 foot far up the pole.