Calculating Time for a Trailer to Move with Constant Friction

[Cincin]

Hi! This is a Maths C problem I have been struggling with for quite some time. I have already spent several hours on this problems and sought assistance. I have got my answer to equal 32mins. However, my teacher has claimed that the answer to this problem is approx 34 minutes. Any help or guidance as to where I have gone wrong would be greatly appreciated. Note : Force of friction remains constant. First image is the question, the following two are my working.

 

[krebs]

I, too, got 31.9 minutes, solving independently. The difference is 4-5%

 

[krebs]

If you read the problem as Daniel is pushing at 15 degrees relative to the ground, in the same direction as the incline, you can get a slightly different answer (32.9 minutes). In that case, his force would be cos(3 degrees) * 1000N. Even if he was pushing at exactly 18 degrees, the answer would still be 32.9 minutes. The reason I reread it this way is because there is an ambiguity in your interpretation. Daniel could be pushing at 15 degrees down on the cart, or 15 degrees up on the cart, although it makes no difference if friction is held constant.

 

[haruspex]

I, too, got 31.9 minutes, solving independently. The difference is 4-5%

I also confirm 31.9. The information that the force of friction is constant is a little surprising, and may be throwing the teacher. If you change the assumptions to: (1) the original force of friction is just able to hold the trailer, and (2) the coefficient of friction is constant, then you get a slightly larger answer.

 

[Cincin]

Awesome thanks for your help @krebs and @haruspex!

 

[Cincin]

I also confirm 31.9. The information that the force of friction is constant is a little surprising, and may be throwing the teacher. If you change the assumptions to: (1) the original force of friction is just able to hold the trailer, and (2) the coefficient of friction is constant, then you get a slightly larger answer.

And yes, I also thought it was strange that they kept friction constant. Shouldn't it increase as the object gains mass?? In any case, I have been asked to assume the Ff is constant so I will :p