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Mr. Wagle goes to work by a bus. One day he falls asleep
when the bus still has twice as far to go as it has already
gone.
Halfway through the trip he wakes up as the bus bounces over
some bad potholes. When he finally falls asleep again, the
bus still has half the distance to go that it has already
travelled. Fortunately, Mr. Wagle wakes up at the end of his
trip.
What portion of the total trip did Mr. Wagle sleep?
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Mr. wagle slept through half his trip.
Let's draw a timeline. Picture the bus route on a line
showen below:
---------------- ________ -------- ________________
Start 1/3 1/2 2/3 End
----- shows time for which Mr. Wagle was not sleeping
_____ shows time for which Mr. Wagle was sleeping
When Mr. Wagle fell asleep the first time, the bus sill had
twice as far to go as it had already gone, that marks the
first third of his trip.
He wake up halfway through the trip i.e slept from 1/3 mark
to the 1/2 mark. He fell sleep again when the bus still had
half the distance to go that it had already traveled i.e 2/3
mark.
Adding up, all sleeping times,
= (1/2 - 1/3) + (1 - 2/3)
= 1/6 + 1/3
= 1/2
Hence, Mr. wagle slept through half his trip.
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