Math problem - picket fences

[Electrons]

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Is this problem just a matter of bad word of choice?

Q: A picket fence is 60 ft long. Its pickets are 1.5 ft apart. If the fence is extended to 80 ft, without adding any pickets, what is the new distance in ft between pickets?

choices:
a) 1 1/8
b) 2
c) 8/9
d) 2 1/8
e) 3

Answer is B, I guessed it correctly, but the solution said there are 41 pickets and 40 sections. How can that be?
It doesn't make sense because 60 / 1.5 = 40, so shouldn't it be 40 pickets instead of 41? Are they leaving out some explanation here?

 

[jaz129]

it says the spaces btwn the pickets are 1.5ft apart soo 60/1.5 would give the amount of spaces.

 

[Electrons]

Thanks. I get it now. 60/1.5 = 40 "spaces apart" not 40 pickets and they got 41 because 1 extra to wrap around the 40 spaces.

 

[Streetwolf]

Yeah, the first picket is placed at distance = 0 ft. The second picket is placed at distance = 1.5 ft. So in the first 1.5 ft you have the first 2 pickets. The 41 pickets / 40 spaces is because the first picket is placed at the 0 ft mark and not the 1.5 ft mark.

They are in a straight line.

There's a similar question regarding trees in a row or something like that. It's like, there are trees in a straight line and a distance of 1.5 ft between them. There are 60 ft from start to end. How many trees? Answer is 41 because the first tree is at 0 ft and not 1.5 ft.

 

[winnie bear]

Yeah, the first picket is placed at distance = 0 ft. The second picket is placed at distance = 1.5 ft. So in the first 1.5 ft you have the first 2 pickets. The 41 pickets / 40 spaces is because the first picket is placed at the 0 ft mark and not the 1.5 ft mark.

They are in a straight line.

There's a similar question regarding trees in a row or something like that. It's like, there are trees in a straight line and a distance of 1.5 ft between them. There are 60 ft from start to end. How many trees? Answer is 41 because the first tree is at 0 ft and not 1.5 ft.

I know this is an old post but I came across the same problem. In a 60 ft long fence, to say that there are forty 1.5ft spaces between pickets is like saying that the pickets themselves don't take up any of the 60 ft space and that pickets don't exist in this "picket fence". Shouldn't the spaces make up only a fraction of the total length? Or am I missing something that's really obvious.

 

[Dental2000]

Use Unitary Method

60 = 1.5

so for 80ft = (1.5/60) * 80

which is 2