Ok so it goes like this...

Billie, a bushwalker, goes on a four day journey. She travels a certain distance on the first day, half that distance on the second day, a third that distance on the third day and a quarter of that distance on the fourth day. If the total distance is 50km, how far did she walk on the first day?

It would be great if you could help us end this argument (if you don't get my answer well your wrong still it doesn't change the fact that I am 110000% correct)

Thanks!

Guest May 15, 2019

#5**+3 **

Let the number of kilometers she traveled on the first day = x

When you say, "a third that distance on the third day and a quarter of that distance on the fourth day," I think "that distance" is x .

\(x+\frac12x+\frac13x+\frac14x\,=\,50\\~\\ x(1+\frac12+\frac13+\frac14)\,=\,50\\~\\ x(\frac{25}{12})\,=\,50\\~\\ x(\frac{25}{12})\cdot\frac{12}{25}\,=\,50\cdot\frac{12}{25}\\~\\ x\,=\,24\)

She traveled 24 kilometers on the first day.

hectictar May 15, 2019

#7**-2 **

Ok, thanks.

The problem was that the question was worded badly with the last bit saying to get a quarter __of__ that distance, so I just halved it through substitution, then got a third of the halved distance, a fourth and so on.

In the end, after a lot of trial and error, I got 29.2682924+14.6341462+4.8780487333333+1.2195122=50km

So I'm *technically *right, but I just did it the long way.

Guest May 15, 2019

#8**+2 **

You solved a different problem. It is kind of unclear what "that distance" refers to.

Also, we can check whether 24 km is a solution (to the problem I solved) like this:

num of km walked on first day + num of km walked on second day + num of km walked on third day +

num of km walked of fourth day = 50 ?

24 + half of 24 + a third of 24 + a quarter of 24 = 50 ?

24 + 12 + 8 + 6 = 50 ?

50 = 50 ?

True

hectictar
May 15, 2019

#6**0 **

I have no idea what those other three stupidumb answers are, the answer was 29.2682924 km on the first day

Guest May 15, 2019

#9**+3 **

Here is the solution to the problem the way you interpreted it:

Let the number of km traveled on the first day = x

\(x+\frac12x+\frac13\Big(\frac12x\Big)+\frac14\Big[\frac13(\frac12x)\Big]\,=\,50\\~\\ x+\frac12x+\frac16x+\frac1{24}x\,=\,50\\~\\ x(1+\frac12+\frac16+\frac1{24})\,=\,50\\~\\ x(\frac{41}{24})\,=\,50\\~\\ x(\frac{41}{24})\cdot\frac{24}{41}\,=\,50\cdot\frac{24}{41}\\~\\ x\,=\,\frac{1200}{41}\\~\\ x\,\approx\,29.268\)

The number of km she traveled on the first day ≈ 29.268

hectictar May 15, 2019

#10**0 **

According to the question, the last answer # 6 is the accurate answer:

(x) + 1/2( x) + 1/6( x) + 1/24( x) =50, solve for x

x = 29 11/41 - Km - she walked on 1st day.

= 14 26/41 - Km on 2nd day

= 4 36/41 - km on the 3rd day,

=1 9/41- Km on th 4th day.

Total = 50 Km

Guest May 15, 2019

edited by
Guest
May 15, 2019

#12**+3 **

Billie, a bushwalker, goes on a four day journey. She travels a certain distance on the first day, half that distance on the second day, a third that distance on the third day and a quarter of that distance on the fourth day. If the total distance is 50km, how far did she walk on the first day?

The meaning of the blue words is ambiguous. So there are multiple different interpretations of the problem. Each interpretation yields a different answer.

I think that the intended interpretation is this:

Billie, a bushwalker, goes on a four day journey. She travels a certain distance on the first day, half that distance on the second day, a third the distance traveled on the first day on the third day and a quarter of the distance traveled on the first day on the fourth day. If the total distance is 50km, how far did she walk on the first day?

There are 2 reasons why I think that is the intended interpretation:

1. All instances of "that distance" in the problem statement would refer to the same thing.

2. The solution would be an integer, and an integer that is divisible by 2, 3, and 4 at that.

hectictar May 15, 2019

#13**+3 **

I agree. The question states "She travels a *certain* distance on the first day, half *that* distance on the second day, a third *that* distance on the third day..."

The usage of the word 'certain' combined with a repeated 'that,' as in referring to the same *certain* distance over and over, implies the same setup to the problem for me.

Anthrax
May 15, 2019