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

[Catron]

Fair enough carrot99 - believe you me I struggled with fractions as well.

If you take a number that is smaller than one, 1/2 for example and say I want to find a 1/2 of 2, the answer is going to be less than 2. Similarly, 2/5 of 3/5 cannot end in a result that is bigger than 3/5, which 2/3 is. To work out this sum multiply the numerators (the numbers at the top of the fractions) together and then multiply the denominators (the numbers at the bottom of the fractions together - 2x3 is 6 (so the answer will be six somethings); 5x5 is 25 so the somethings is 25ths - and so your answer is 6/25, or six twentyfifths.

Anyway, I'm off to do something else. I hope this helps but if not, perhaps someone who is better at explaining these things will be around.

[Rollo]

Carrot. Let's assume your calculation is correct and that the total distance is 140 miles.

Then going back to the original question:

Day 1 they travel 1/5 of the distance. That's 28 miles. so there is still 112 miles left to go.

Day2 they cover 1/4 of the 112 miles left. That's 28 miles. So there are still 84 miles left to go.

Day3 they cover 2/5 of the 84 miles left. That's 33.6 miles. So there are still 50.4 miles left to go.

Day 4 they cover 1/2 of the 50.4 miles left. that's 25.2 miles. So there are still 25.2 miles left to go.

But the questions says there are only 14 miles left to go.

So it follows that the 140 miles we started with was not correct.

[greengoddess]

I am sure glad I went out last night after posting my answer!!! It looks like world war 3 broke out.
However I admit my answer was wrong.
The total distance was indeed 77.77777 miles
Less the 14 not travelled.
63.777777

[janus123]

Day1 - travel 1/5 of X
Day2 - travel 1/4 of 4/5 X = 1/5 X
Day 3 - travel 2/5 of 3/5 X = 6/25 X
by now they've travelled (1/5+ 1/5 + 6/25) X = 16/25 X
Remainder is 14/25 X, so
Day 4 - travel 7/25X

X- (1/5 + 1/5 + 6/25 + 7/25)X = 14
X(1-23/25)=14
X=14 x 25/2 = 175 miles

[Catron]

Oh no - not again. Janus123 - your sum is correct up to the point where you take 16/25 away from 25/25 and make 14/25; it is only 9/25 remaining at that point. Please believe me the question has been answered correctly a number of times before and is 63.77 miles (to 2.d.p)

[Annieh4]

Excuse a newcomer but isn't this correct?

Day 1 � travelled 1/5 of the distance or 4/20
Left to travel � 16/20
Day 2 � travelled � of 16/20 = 4/20
Left to travel � 12/20
Day 3 � travelled 2/5 of 12/20 � 6/20
Left to travel � 6/20
Day 4 � Travelled � of 6/20 = 3/20
Left to travel � 3/20 = 14 miles
1/20 = 14/3 = 4.666666miles
Have travelled 17/20 (as 3/20 left to go) so distance travelled = 4.666666 x 17 = 79.33333 recurring

If not, where did I go wrong?

[Catron]

Annieh4 - 2/5 of 12/20 is not 6/20 - it is 24/100 or 12/50 or 6/25.

MU120 for you? Think you need it!! ha ha.

[Annieh4]

Thanks Catron. I did that bit so many times and got the same answer every time! Of course it is wrong! 2/5 of 12/20 cannot be 6/20 - that is 1/2!