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[Cazzaroo]

Please can anybody help with the below questions?

1. A man sets out to travel from one town to another. On the first day he covers one half of the total distance. On the second day he covers one third of the remaining distance. On the third day he covers one third of the remaining distance and on the fourth day he covers one half of the remaining distance. He now has 37 miles left to reach the second town. What distance has he travelled so far?

2. The letters below represent integers. Work out what number is represented by each letter. Clue: R = 2G

E I G H T
T H R E E
N I N E +
_____________
T W E N T Y

3. Each of the following words except one is an anagram of another word. Which one has no English anagram?

SAILED PRESENT STERLING REGINA VIKING

4. The following letters can be rearranged to spell five words that refer to an event which is compared to a large animal. Here are the letters, what is the phrase?

E E A A A W T O M F H I L

5. Here is a word written both vertically and horizontally. Complete the word square so that it reads both across and downwards with good English words.

F O R T

O

R

T

[lelliej]

3. viking

[mac44]

5 FORT

OBOE

ROAN

TENT

[juliefer]

4. A whale of a time.

[flamingo97]

Yes good one mac44. I had another:

FORT, OBOE RODE and TEEM. Must be quite a few I reckon.

[CNB]

1. 296 miles

[juliefer]

1. 259

[mac44]

Good thinking flamingo97

How about FORT OBEY REAR TYRO

[juliefer]

2. The numbers 0 to 9, excluding the 6, are represented by the letters W T G N R I Y E and H.

[halfadaily]

I make the distance travelled 296 miles so far:

Day one; 166.5 miles

day two; 55.5 miles

day three; 37 miles

and day four; 37 miles

total distance travelled 333 miles

let's hope he had a car

[gen2]

Sorry to disagree.
Let total distance = x
Day 1 covers 1/2 x = 18/36 x
Day 2 covers 1/3 * (1/2 x) = 1/6 x = 6/36 x
Day 3 covers 1/3 * (1/3 * (1/2 x)) = 1/18 x = 2/36 x
Day 4 covers 1/2 * (1/3 * (1/3 * (1/2 x))) = 1/36 x

Total covered = (18/36 + 6/36 + 2/36 + 1/36) x
= 27/36 x
= 3/4 x

Therefore distance remaining = 1/4 x = 37 miles

If 1/4 x = 37,
then 3/4 x (the distance covered) = 3*37
= 111 miles

Answer: Distance covered = 111 miles

[halfadaily]

I still maintain that I'm right. Let's assume the total length of the journey is 333 miles. On day one he covers half this distance covering 166.5 miles. On day two he travels 1/3 of 166.5 miles totaling 55.5 miles.

This leaves 111 miles left to travel at the start of day three. He travels 1/3 again which is 37 miles, leaving 74 miles to travel at the start of day four.

On day four he travels 1/2 of the 74 miles, totalling 37 miles in the day. Therefore at the start of day five he has just 37 miles left to travel.

So the distance traveled on the first four days adds up to 296 miles.

No magic formulae used to get this figure, I just played around with a few starting figures until it all clicked.

[mohill]

I agree with halfadaily and CNB.

Because of the fractions involved it is convenient to think of the daily distances in 36ths.

Day 1: he does 1/2 the distance, ie 18/36. This leaves 18/36 to be done.

Day 2: he does 1/3 of 18/36, ie 6/36. He has now done a total of 24/36, leaving 12/36 to be done

Day 3: he does1/3 of 12/36, ie 4/36. He has now done a total of 28/36, leaving 8/36 to be done

Day 4: he does 1/2 of 8/36, ie 4/36. He has now done a total of 32/36, leaving 4/36 to be done.

4/36 is the same as 1/9. So 1/9 of the whole journey is 37 miles

So the 8/9 he has done is 8 times 37, ie 296.

[crofter]

Sorry gen2, but you have not used the given information correctly. On day 3, he covers one third of the remaining distance - not one third of what he travelled the previous day!

Otherwise - I like your algebraic style!

[Clayhead]

I'm with halfadaily - 296 travelled, 37 to go.

[gen2]

Thanks crofter, I see the error of my ways. I plead the lateness of the hour in mitigation.

[Buzzie]

Work it backwards from day 5 when he has 37 miles to cover.

Day 4 he has covered half the remaining distance, so day 4 = 37 miles also

Day 3 he covers one third of the remaining distance to LEAVE himself 74 miles, which must therefore be 2/3 of the distance he started with, meaning he covered 37 miles

Day 2 he covered one third of the remaining distance to leave himself 111 miles, which again is 2/3 of the distance he started with, meaning he covered 55.5 miles

Day 1 he covered half the remaining distance to leave himself 166.5 miles so he must have covered 166.5 miles on day 1.

His total is therefore 166.5+55.5+37+37 = 296 miles!!