A bike rider covers 100 km at a speed of 75 km/h. At what speed does the rider have to drive for the next one hour to get an average speed of 90 km/h? 

Alternate MethodTime taken to cover 100 km at a speed of 75km/hr 

⇒ Distance/speed = 100/75 = 4/3 hr

Let the speed of the rider = y km/hr

Time = 1 hr

Distance covered by bike rider = Speed × Time

⇒ y × 1 = y km

Average Speed = total distance/total time

⇒ 90 = (100 + y)/(4/3 +1)

⇒ 90 × 7/3 = 100 + y

⇒ y = 110

Speed = Distance/time

⇒ Speed = 110/1 = 110 km/hr

∴ The speed of the rider to drive for the next one hour is 110 km/hr.

Given Data:

Distance covered = 100 km

Initial speed = 75 km/h

Desired average speed = 90 km/h

Concept:

Average speed = Total Distance / Total Time

Calculation:

Time taken for first part of journey = Distance covered / Initial speed

⇒ Time = 100 / 75 = 1.33 hours

Total distance to be covered for an average speed of 90 km/h in (1 + 1.33) hours

⇒ Total distance = 90 × 2.33 = 209.7 km

Distance to be covered in the next one hour = Total distance - Initial distance

⇒ Distance = 209.7 - 100 = 109.7 km

Speed = Distance / Time

⇒ Speed = 109.7 / 1 ≈ 110 km/h

Hence, the rider has to drive at a speed of approximately 110 km/h for the next one hour.