"Machine 2 is overall $50\%$ slower than machine 1, which takes one hour on machine 1. Considering the following sentence, is it mathematically correct?
"Machine 2 is overall 50% slower than machine 1, i.e. a job that takes 1 hour on machine 1 takes 1.5 hours on machine 2."
My interpretation is as follows: Let's say Machine 1 produces 10 parts per hour. Machine 2 is 50% slower, so it produces 5 parts per hour. Therefore it will take Machine 2, 2 hours to produce 10 parts instead of 1.5.
 A: The sentence "A is 50% slower than B" can be problematic.
In general, an increase of (say) $20\%$ amounts to multiply the original value by $1 + 20/100 = 1.2$
And a decrease of $20\%$ amounts to multiply by $1 - 20/100 = 0.8$
Now,  I'd read "A is 50% slower than B" as a decrease of speed, hence $s_A = (1- 50/100) s_B  = \frac12 s_B $
where $s_A,s_B$ are the speeds.
Hence, I'd agree with you.
Now, if instead of speaking of speeds we speak of its inverse, pace ("slowness") , the amount of time it takes to complete a job, then we could read "A is 50% slower than B" as an increase of pace, hence $p_A = 1.5 p_B$ . Which would agree with your original sentence.
A: Ordinarily this sort of language is ambiguous for a number of reasons. However, in this case, there is a given clarification in the problem as quoted by the OP.
One curiosity about the idiom used is that "fifty per cent slower than" suggests less slow. This gives an interpretation where machine two is actually faster than machine one.
