A travels at the speed of 5km./hr. He reduces speed every hour by 1/4 km./hr. How much time he take for 50km?

Answer 1

first hour he travels 5 km
second hour 4.75
so 5 + 4.75 + 4.5 ---------5 - (n-1)0.25
this series is arthimetic rogression
we want to know n when the sum is 50 km
the sum of the progression is
s = n/2[2a + (n - 1)d]
a = 5 d = -0.25 and s = 50
50 = n/2[2(5) +(n - 1)(-0.25)]
50 = n/2[10 - 0.25n + 0.25]
100 = n[10.25 - 0.25 n]
100 = 10.25 n - 0.25n^2
25n^2 - 1025n + 10000 = 0
n^2 - 41n + 400 = 0
n^2 - 25n - 16n + 400m =0
n(n - 25) - 16(n - 25) = 0
(n - 25)(n - 16) = 0
n = 25 or 16
n = 16
25 is to be ignored. As common difference d (-0.25) is negative, sum of 17th to 25 terms will be zero and again the sum will be 50.
So he takes 16 hrs to travel 50 km

Answer 2

He needs to go 50km. If he did not reduce speed it would take 10 hours. At 5 km/hr he travels for 1 hour. There are now 49 km left on the trip. At his new speed he is going 4.925 km per hour so he has gone 9.925 km after 2 hours. Then his new speed is 4.9 km/hr so he has gone 14.825 km after the 3rd hour. Then he travels at 4.65 km/h for an hour and goes a total of 19.475 km after 4 hours. Then he travels at 4.4 km/h for an hour and goes a total of 23.875 km after 5 hours. Then he travels at 4.15 km/h for an hour and goes a total of 28.025 km after 6 hours.

If you have more patience than I do you could keep nibbling away at this 1 hour at a time. Or if you remembered the correct way to handle this algebraically you would already know the answer.

Answer 3

Answer: 16hours.
I'm sure there is a much easier way of doing it.. but this is what I did:
In the 1st hour, it travels at 5km/hr.. therefore it travels 5 km in the first hour.
In the second hour, it travels 4.75km /hr.. therefore it travels 4.75 km in the second hour (9.75 km total)......
Keep going like this until the total 50km is reached.. Turns out to be after the 16th hour.

Answer 4

I get 16½ hours by working it out the long way.
At the end of 16 hrs. he has gone 49½ km. and reduced
his speed to 1 kph; another half hour brings him to 50 km.
It would be fun to see how long it takes him to go 53 km!

Answer 5

16 hours.

Answer 6

1/4 of 50 = 1/4 of 50 =12.5, 50-12.5=37.5, one hour
1/4 of 37.5= 1/4 of 37.5=9.375, 37.5-9.375=28.125 hour 2
1/4 of 28.125=7.03,28.125-7.03=21.1 hour 3
1/4 of 21.1=5.275, 21.1-5.275=15.825 hour4
1/4 of 15.825=3.96, 15.825-3.96=11.865 hour 5
1/4 of 11.865=2.97, 11.865-2.97=8.895 hour 6
1/4 of 8.895=2.22, 8.895-2.22=6.675 hour 7
1/4 of 6.675=1.67. 6.675-1.67=5. hour 8
1/4 of 5=1.25. 5-1.25=3.77 hour 9
1/4 of 3.77=0.94, 3.77-0.94=2.83 hour 10
1/4 of 2.83=0.71, 2.83-0.71=2.12 hour 11
1/4 of 2.12=0.53, 2.12-0.53=1.59 hour 12
1/4 of 1.59=0.4, 1.59-0.4=1.19 hour 13
1/4 of 1.19=0.29, 1.19-0.29=1.61 hour 14 ) I hope you get the concept.)