Question 591614: If I walk 50kms. The first day I walk so far the next day I walk half as much and on the 3rd day I walk a third of the day before and on the fourth day a fourth of the day previously, How far did I walk the first day
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you don't have enough information to come up with a single answer.
you can solve this problem, but you will need to know either:
total time
or:
total distance
the basic formula is RT = D
R = rate of travel
T = time
D = distance
i don't know what you mean by kms.
if that's kilometers per second then it's not realistic.
the average person walks 3 miles per hour which is roughly equivalent to 5 kilometers per hour.
that would be 5kph.
i will assume 5kph.
assuming that, this is how it will work out.
the distance traveled is shown as follows:
day 1 equals D
day 2 equals D/2
day 3 equals (D/2)/3 which is equal to D/6
day 4 equals (D/6)/4 which is equal to D/24
the total distance traveled over the 4 days is:
D + D/2 + D/6 + D/24
this comes out to be 41D/24 total.
D = 24D/24
D/2 = 12D/24
D/6 = 4D/24
D/24 = D/24
since they now have a common denominator, just add up the numerators and divide the total by the denominator to get (24 + 12 + 4 + 1)/24 which is equal to:
41D/24
the rate is always the same (5kmph)
the total time is calculated by use of the formula to get:
total time * rate = total distance
we solve for time to get:
total time = total distance / rate
since total distance is equal to 41D/24, and since rate is equal to 5kmph, this becomes:
total time = (41D/24) / 5 which becomes 41D/(24*5) which becomes .3416666667D
your final equation is:"
total time = .3416666667D
you have 2 unknowns in one equation.
best you can do is make an assumption about total time or about total distance.
when you know one of them, you can find the other.
you can't, however find both.
not with the information given.
i assumed the total time was 4 hours.
the equation of:
total time = .3416666667D becomes:
4 = .3416666667D
i then solved for D to get:
D = 4/.3416666667 = 11.70731707 kilometers
that distance only applies if the total time is 4 hours.
change the total time and the distance changes.
assuming that the total time is 4 hours, the day by day breakdown was:
day distance (km) rate (kmph) time (hours)
1 11.70731707 5 2.341463415
2 5.853658537 5 1.170731707
3 1.951219512 5 0.3902439024
4 .487804878 5 0.0975609756
total 20 --- 4
total distance was 20 kilometers and total time was 4 hours.
distance traveled the first day was 11.70731707 kilometers
this value is only accurate if the total time was assumed to be 4 hours.
once again, there is not enough information provided to give an exact answer.
you have too many unknowns and not enough equations.
to get 1 answer, you need to have as many equations as you have unknowns (variables).
you had 2 unknowns (time and distance) with only 1 equation (rate * time = distance).
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