Problem applying Newtons third law

[Neil Melnick]

Homework Statement

Two people each with a mass of 70kg are wearing in line skates and holding opposite ends of a 15m rope. One person pulls forward on the rope by moving hand over hand and gradually reeling in more of the rope. In doing so, he exerts a force of 35N (backwards) on the rope. This causes him to accelerate toward the other person. Assuming that the friction on the skaters is negligible, how long will it take for them to meet? Explain.

Homework Equations

F=MA and D= T x init. Veloc.+ 0.5 AT²

The Attempt at a Solution

Book says 7.7, I say 5.5. Book splits the 35N between the two masses, I say equal and opposite means 35N acts on each. Consulted with several engineers, no consensus. Help!

 

[TSny]

Welcome to PF!

Your answer of 5.5 seconds is correct. The tension in the rope will be 35 N. Each person is acted on by a 35 N tension force from the rope.

 

[Orodruin]

There will be 35 N forces acting on both persons. There is no "splitting".