visit to father christmas

[alison6399]

A group trekking across Lapland to vivit Father Christmas cover one fifth of the total distance of the 1st day.

The next day they cover a quarter of what's left..

The following day they cover 2/5 of the remainder and on the fourth dayhalf of the remaining distance.

They now have 14 miles left.

How far have they travelled.

Please explain reason behind answer.

Thanx

[greengoddess]

One fifth + One fifth +Two fifths leaves one fifth.
14 miles = One fifth.
70 Miles in total.

[greengoddess]

Sorry that is wrong will try again.

[The Builder]

x=distance
1st day 10x/50 miles
2nd day 10x/50 miles (quarter of 40x/50)
3rd day 12x/50 (two fifths of remaining 30x/50
4th day 9x/50 (half of remaining 18x/50

9x/50 remain =14 miles

gonna be fractions of a mile I reckon......:o(

[greengoddess]

1st day = one fifth
2nd day= one fifth
3rd day= two fifths
4th day=one tenth.
Total =nine tenths so one tenth =14 miles. total distance 140 miles.
At least I think so until someone proves me wrong!!

[The Builder]

I'm not in a position to talk Greengoddess - but I think your 3rd day is wrong - it should two fifths of three fifths ?

[Rollo]

I agree with builder's calculations.

9x/50 = 14 miles, so therey have travelled 41x/50 miles

=63.7777777777777777777777777777777777778 miles

But it seems a strange answer.

[greengoddess]

Hi Builder. Two fifths of three fifths leaves one fifth.
Half of one fifth is a tenth. I am totally lost now but I still think I am right.

[valawil]

Surely the equation is simply 14 x 5 which equals 70.
Travelling 1x 5th then a quarter is another 5th then 2 x 5th's so the remaining 14 miles is the last 5th.

[Clayhead]

Valawil, the 3rd day's distance is "2/fifths of the remainder".

[Clayhead]

Builder and Rollo are CORRECT

Working backwards, on the 4th day they cover 1/2 of the remainder - if the distance after the 4th day is 14 miles, they must cover 14 miles on the 4th day ( a half of what was remaining after day 3).

On the 3rd day they cover "2-fifths of the remainder", so the balance after day 3 (28 miles) must represent 3-fifths of what is remaining after day 2. So the distance travelled on day 3 is 18.667 miles, which represents 2-fifths of the distance remaining after day 2.

On the 2nd day, they covered "a 1/4 of what's left". We know that the balance after day 2 is 46.667 miles (28 + 18.667).
This must represent 3-quarters of what is left after day1, so on day 2, they cover 15.556 miles (1/3 of 46.667).

On day 1, they cover "1/5th of the total distance". We know that the balance at the end of day 1 is, as calculated, 62.223 miles and this is 4/5ths of the total distance - so they cover 15.556 miles again, being 1/5th.

So, I think that the total distance is 77.779 miles BUT that is not what is asked. The question asks "How far have they travelled?" and the facts do not state that they have travelled the complete distance- they were left with 14 miles, so, as Rollo and Builder said, they travelled 63.779 miles !!

[carrot99]

Greengoddess I agree with you:

day 1 1/5 = 20%
day 2 1/5 = 20%
day 3 2/5 of remaining 3/5 ie 2/3 of 60% = 40%
day 4 1/2 of remaining 20% = 10%
day 5 final 10% or 14 miles

10% = 14 miles, 100% = 140 miles
distance already travelled 126 miles

[Catron]

How does 2/5 suddenly become 2/3, carrot99? This is where greengoddess made a mistake - The Builder, Rollo and Clayhead are all right. 63.7 recurring is the answer, improbable as it sounds.

[duckshoot]

The Answer is 77.777777 (77 7/9)

Working back
1/5 on Day 1; 15.555555 leaves 62.22222

1/4 on Day2; 15.555555 leaves 46.66666

2/5 on Day 3; 18.666666 leaves 28

1/2 on Day 4; 14 leaves 14

[carrot99]

On the third day they cover two fifths of the remainder- we know they have already covered a fifth on both the first and second days so the remainder must be three fifths. (40% done, 60% to go).

On the third day they must cover another 2/5 of the remaining 3/5. Two out of three is where I get 2/3. So 2/3 of the remaining 60% is 40%. Leaving 20% - half for the fourth day and the final 10% outstanding as the final 14 miles.

Hope that helps.

[Catron]

No, Carrot99 - sorry but you are still getting this wrong - on the third day (with as you say 60% of the journey to go) they go 2/5 of that remaining 60% - 2/5 of 60% is 24% (just as 2/5 of 3/5 is 6/25).

Duckshoot - that is the total distance of the journey - the question asks how far they have travelled with 14 miles of the distance still to go. 77.7 - 14 is 63.778 (to 3 d.p).

[carrot99]

They go two fifths of the remaining three fifths! Two fifths of three fifths = two thirds.
So not 2/5 of 60% but 2/3 of 60% = 40%.

OK?

[Catron]

2/5 of 3/5 is NOT 2/3!!

[carrot99]

Another way - on the third day they go two fifths of the total distance outstanding - 2/5 of 100% = 40%!

[Catron]

Are you doing this deliberately, carrot99?

The question clearly states that they go 2/5 of the remaining distance which is 60% - 2/5 of 60% is 24%.

I will not be saying this again - you are wrong when you say they go 40% on the third day.

Sorry Alison - I hope you have not been troubled with an e-mail for each of these responses.

[carrot99]

Catron - my fractions are very rusty so isn't 2/5 of 3/5 2/5 x 5/3 = 10/15 = 2/3??