Last week, I travelled from Chicago to Des Moines. On the first day I travelled one quarter of the distance. On day two, I travelled one half of the remaining distance. On day three, I travelled three quarters of the remaining distance. Yesterday I travelled one third of the remaining distance. I now have 21 miles left to travel. How far is it from Chicago to Des Moines in total?
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Chicago to Des Moines4 guesses to Chicago to Des Moines |
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May 14th, 2012 | Category: 
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350 miles,
No Carole, that’s not it, but you’re very close. Redo your math and try again.
336 miles
336 miles from Chicago to Des Moines is correct, Anant.
On the first day I travelled one quarter of the distance (84, leaving 252). On day two, I travelled one half of the remaining distance (126, leaving 126). On day three, I travelled three quarters of the remaining distance (94.5, leaving 31.5). Yesterday I travelled one third of the remaining distance (10.5). I now have 21 miles left to travel.
To work these numbers out, it is easiest to start at the end and work backwards.
Yesterday I travelled 1÷3 of the distance to leave 21 miles, therefore there were 31.5 miles (=21 x 3÷2) at the start of yesterday.
On day 3 I travelled 3÷4 of the distance to leave 31.5 miles, therefore there were 126 miles (=31.5 x 4) at the start of day 3.
On day 2 I travelled 1÷2 of the distance to leave 126 miles, therefore there were 252 miles (=126 x 2) at the start of day 2.
On the first day I travelled 1÷4 of the distance to leave 252 miles, therefore there were 336 miles (=252 x 4÷3) at the start of the first day.
You are today’s winner.