Carla Denyer - Do As I Say Not As I Do?
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visit to father christmas
28 Answers
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
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
Answers
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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 !!
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 !!
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.
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.
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).
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).
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.
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.
