Question

ii.
A man set out on a cycle ride of 50 km. He covers 5 km in the first hour and during each
successive hour his speed falls by - km/hr. How many hours will he take to finish his ride?
4​

Answer 1

Answer:

Step-by-step explanation:

The time taken by man to cover the distance would be 16 hours.

Answer 2

Answer:

Step-by-step explanation:

1) Total distance of cycle ride = 50 km.

2) Distance covered in first hour = 5 km

Distance covered in second hour = 4.75 km

Distance covered in third hour = 4.5 km

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.

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Distance covered in nth hour = 5-(n-1)/4 km

3) The total distance covered would be 5 + 4.75 + 4.5 +.......... + 5-(n-1)/4

4) The sum should be 50 km

5) This series is an AP with a = 5 km and d = -0.25 km

6) The distance covered in n hours is

Sₙ = (n/2) (2a + (n-1)d)

Sₙ = (n/2) (10 + (n-1)(-0.25)

50 = (n/2) (10 -n/4 +1/4)

50 = (n/2) (41-n)/4

400 = n(41-n)

n² -41n +400 = 0

(n-16)(n-25) = 0

7) Hence, values of n =16,25.

8) Discarding n =25, since after 20th hour, the speed would become zero and can't be decreased further.

9) Hence, the time taken would be 16 hours