Question

If a bike rider starts at 14 kmph and he increases his speed in every 3 hours by 4 kmph (speed increases instantaneously after 3 hrs and then remains constant for the next 3 hrs), then what is the time taken by the bike rider to cover 250 km?

• A. 12 hours 40 mins
• B. 12 hours 30 mins
• C. 12 hours 25 mins
• D. 12 hours 20 mins

Answer 1

The correct option is D

12 hours 20 mins

Initial speed of the bike rider = 14 kmph

Distance covered in 1st 3 hours = 14 x 3 = 42 km.

After increasing, 4 km/hr for every 3 hours period,

Distance covered in 2nd 3 hours period = (14+4) $\times$ 3 = 54 km.

Distance covered in 3rd 3 hours period = (18+4) $\times$ 3 = 66 km.

Distance covered in 4th 3 hours period = (22+4) $\times$ 3 = 78 km.

Total distance covered = 42 + 54 + 66 + 78 = 240 km

Remaining km to cover = 250 - 240 = 10 km.

Speed in 5th 3 hours period = 30 kmph

Time to cover 10 km at 30 kmph = $\frac{10}{30}$ hours = $\frac{1}{3}$ hour = 20 mins.

Now, the total time taken by the rider for 250 km = (3 + 3 + 3 + 3 + 0.33) = 12 hours 20 mins