We all know that "Peter Piper picked a peck of pickled peppers", but how long did it take him?

Peter and Paul together can pick a peck in 20 minutes, and Paul and Patrick together can pick a peck in 30 minutes. Peter and Patrick however, take 40 minutes to pick a peck together.

How long does it take Peter to pick a peck of pickled peppers by himself?

48 mins

work showed below

Peter=p, Paul=q, Patrick=r. Consider how many peppers they pick in 120 mins.
1. p+q=6
2. q+r=4
3. p+r=3
Subtract 1 and 2 gives 4. p-r=2
adding 3 and 4 gives 2p=5 or p=2.5
So Peter picks 2.5 peppers in 120 mins or 1 pepper in 48 mins.

a = Paul, b = Patrick, c = Peter
Make "the job" = travelling 1 mile:

@a+c.........1..........>20 : 20(a+c) = 1 [1]
@a+b.........1..........>30 : 30(a+b) = 1 [2]
@b+c.........1..........>40 : 40(b+c) = 1 [3]
Expand:

3 equations, 3 unknowns.
Solve (elimination or substitution) to get:
a = 7/240, b = 1/240, c = 1/48

c = Peter = 1/48 of "job" in 1 minute,
so takes 48 minutes by himself.

That one was a dilly!

A dilly!!! Good one Sue.

Thanks curly! Puns are our bread and butter here.