A girl wants to climb down a rope. The girl weighs 100 lbs but the rope only provides an upward force of 60 lbs. What is the maximum acceleration at which the girl can slide down the rope without it breaking?

A girl weighs 100 lbs. She is climbing down a rope that only provides 60 lbs of force upwards. What is the maximum acceleration whe can slide down without the rope breaking?

I think you're looking for the minimum acceleration she must attain, not the maximum.

Draw a free body diagram. Acting downward on her is the force of gravity (her weight) and upwards is the resistance -of the rope, which is 60 pounds-force. The difference is due to her acceleration, which is her mass times her acceleration. Be sure to put things into proper units (keep your pound-force and pound-mass units straight).