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## Tuesday, January 15, 2008

### The Lawn Boys

If a boy and a half can mow a lawn and a half in a day and a half, how many and a half can mow a dozen and a half in a week and a half?

Anonymous said...

one

Anonymous said...

it doesn't work out evenly...i've tried it various ways getting the same answer...it's asking how many boys does it take to mow a dozen and a half (18) lawns in a week in a half (10.5 days).

1 boy can mow 1 lawn in 1.5 days
2 boys can mow 2 lawns in 1.5 days
2.5 boys can mow 2.5 lawns in 1.5 days
when figuring out how many boys can mow a certain number of lawns in a certain amount of day (i've done pictures and charts) i've realized that 10.5 days divided by 1.5 (the original given amount of days) i get 7...so 7B = L we know 18 = the number of lawns so pluggin it in 7B = 18...B=18/7= 2.57boys it doesn't work out perfectly

Drekab said...

If 1 boy can mow 2/3 of a lawn in 1 day.
Then 1 boy can mow 5 lawns in 7.5 days.
And 2.5 boys can mow 12.5 lawns in 7.5 days.

So the answer is two. (How many and a half boys)

Erik said...

One of the anonymous posters above was correct that the result is not an integer value.

Based on the introduction of the problem a single boy can mow a single lawn in 1.5 days, or 2/3 lawn per day (1 1/2 boys complete 1 1/2 lawns in 1 1/2 days--if you take away the 1/2 boy then during the same amount of time (1 1/2 day) one half of one lawn will not be mowed, meaning that a single boy needs 1 1/2 days to mow one lawn.)

"A dozen and a half" is the same as one and one half dozen, or 18, and a week and a half is 10.5 days. The total number of lawns that need to be mowed each day is 18/10.5 or 12/7--this is 'lawns per day'. Divide the total number of lawns per day by the number of lawns a single boy can mow in a day to find the number of boys needed to complete the task: (12/7)/(2/3) = (12/7)•(3/2) = 36/14. We must then subtract one half boy from this result to come up with the final answer because the question asked for "How many and a half?": 36/14 - 7/14 = 29/14, or just slightly more than 2 boys.

One of the 2 boys could bring along a dog with an upset stomach to eat enough grass to make up for that 1/14 of a boy. ;-)

ericanpro said...

I think the puzzle would be better with a slight change of the original question:

Here my proposal:

If a boy and a half can mow a lawn and a half in a day and a half, how many boys are needed to mow a dozen and a half in 7 days and a half?

The answer is "2 and a half".

reasoning:
1 boy can mow 1 lawn in 1.5 days
1 boy can mow 5 lawns in 7.5 days
2.5 boys can mow 12.5 lawns in 7.5 days

Anonymous said...

I think you are missing the fact that it says a Week and a Half.
That is 1.5 weeks which is 10.5 days (not 7.5).

Anonymous said...

How can 2.5 boys mow the lawn?

You have to round up. Half a boy can't do anything.

JP said...

i would like 2 see half a boy mow a lawn

zvl_dnlv said...

there is no answer for this problem