Question

- 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 1/4 km/hr. How many hours will be take to finish his ride?​

Answer 1

Given: Total distance covered = 50 km

Distance covered in the first hour = 5km

Each successive hour his speed falls by = 1 km/4 hr

To find: Hours taken to finish his ride

Distance covered in the second hour =5-1

4

= 20 -1

4

= 19/4

= 4.75 km/hr

Similarly, distance covered in the third hour = 4.50 km/ hr

So, d = 1/4 (1)

This is an AP form

5, 4.75, 4.50,

Here, a= t1 =5

t2 = 4.75

t3 = 4.50

d = t2 -t1 = 4.75 - 5 = -0.25 (2)

Here, Sn = 50

So, Hours to finish cycle ride = n =?

Sn = n [2a + (n-1)d ]

2

50 = n [2×5 + (n-1) (-0.25)]

2

50×2 = n [10 + (n-1) × 1/4]

(from (1)/& (2) d=1/4)

100×4 = 10n + n² - n

400 = 9n + n²

n² + 9n - 400 = 0

n² + 25n -16n -400 = 0

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

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

n = 16 or -25

Hours can never be negative.

So,

n = 16

Therefore 16 hours will be taken to finish his ride.

Answer 2

Answer:

The answer is given in the following attached picture :