The Problem

If a man, A, who weighs 11 stone
leaves from his home at 8:30 in the morning
in a car whose consumption is 16.25 mpg
at an average speed of 40 m.p.h.
to his office which is 12 miles away
and he stops for a coffee on the way for 15 minutes
and also puts air in one of his tyres
which has a slow puncture
letting out air at a rate of 2 lbs per square inch
per mile travelled
when the car is moving at 32 m.p.h.
and he picks up a hitch-hiker B
who weighs 14 stone plus suitcase
But hitch-hiker B who is a political activist
distributes leaflets from his suitcase
each of which weigh an ounce
at the scale of 2 leaflets per person
at every bus stop
and every vehicle on either side of them
at every red traffic light during the journey
which includes 20 bus stops
with an average of 6 people per stop
5 lorries each with a passenger
one of which exchanged a Yorkie Bar
weighing an ounce for 12 of the leaflets
and 2 coaches each containing 51 people
7 of which from one coach returned the leaflets
and 16 people from the other coach
who asked for a further leaflet
each for a member of one of their families
Assuming that man A
then had to travel a further 2.86 miles
out of his way to drop off hitch-hiker B
how late would man A be
in arriving at the office by 9:30 a.m.?
If he still had 6 miles to travel
and his watch was running 23 minutes slow
but the clock at the office was running
2 minutes faster than his
was in fact 17 minutes and 3 secs ahead
of the correct time
which was 2:30 in the morning in Caracas
If when 5 miles from the office
he telephoned his boss
to apologize for being late
but was told by his boss C
to pick up a package 2.63 miles away
from his present location
and deliver it to client D in Bristol by train,
by 4:30 that afternoon
and at the same time man D
was mistakenly told to come to London
to receive same package from man A
Now man A's train, train 1,
left 30 mins. late
but man D's train, train 2,
left 5 mins early
so when the trains passed each other
train 1 was travelling at 75 m.p.h.
to make up for lost time
and train 2 was travelling at 52 m.p.h.
Would man A reach Bristol earlier or later
according to his watch
which was now running 5 mins. slower
than man D's would have been
had he not got off the train
and checked the correct time
at a station between Bristol and London
and stopped to phone A's boss, man C
to double check A would be there to meet him
and discover his mistake
catch next train, train 3, back to Bristol
which unlike A's train 1
which stopped at 4 stations on the way
for 6 mins each stop
was an express train
D's train caught up with A's train 1
4 miles from Bristol
As the trains drew alongside each other
A's train was travelling at 12 m.p.h.
and D's train was travelling at 13.6 m.p.h.
and man A was sat in the front
How long would it take to fill the bath?