Logarithm help?

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If the question is stated accurately, it takes 5 hours. But that is too easy.
I think it's supposed to be 10% of the distance in the first hour,
10% of the remaining distance in the second hour,
10% of the remaining distance in the third hour,
etc.

x = starting distance
0.10x traveled in the first hour; 0.90x distance remains.
0.10(0.90x) traveled in the second hour; 0.90(0.90x) distance remains.
0.10(0.90²x) traveled in the third hour; 0.90(0.90²x) distance remains.
etc.

After n hours, 0.90³x distance remains.
0.90ⁿx = 0.5x
0.90ⁿ = 0.5

take log base 0.90 of both sides
n = 6.578813479
It takes about 6.6 hours to travel halfway....Show more

I don't see the use of logarithms into this.It seems a simple problem,
If 10 % of his/her journey is completed in 1 hour than remaining 90 % will be completed in 9 hrs.So,the total time required to complete journey will be 9+1 =10 hrs.
So ,half of the journey will be done in 10/2=5 hrs....Show more

if a person moves 10% of the distance in one hour, then 90% remains...

(0.90)^n = (0.50)

n log (0.90) = log (0.50)

n = [log (0.50)]/[log (0.90)] ≈ 6.5788 hours

check...do something...Show more