Answer:
see below
Step-by-step explanation:
The equation to determine the work time is
1/a+1/b = 1/c where a and b are the times alone and c is the time together
1/80 + 1/30 = 1/c
Multiply by the least common denominator to clear the fractions, which is 240c
240c(1/80 + 1/30 = 1/c)
3c+8c = 240
11c = 240
Divide by 11
11c/11 =240/11
c = 240/11 minutes
c=21.81818
Approximately 22 minutes


Now before taking the inverse tangent of both sides, recall that

where

is any integer. This means that when taking the inverse tangent of

, instead of just

, we would end up with

So after doing so in the equation above, we're left with

As

can be any integer, including negative integers, we can simply write
speed = distance/time
speed = 8/24 = 1/3 km per minute