A motor car starts with the speed of 70 km/hr with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?

### Concept & Logic When speed changes in discrete time intervals, calculate the distance covered in each interval cumulatively until the target distance is reached. $$Distance = \sum (Speed_i \times Time_i)$$ ### Step-by-Step Solution 1. **Calculate Distance for First Interval (Hours 1 & 2):** * Speed = $70$ km/hr. Time = $2$ hours. * Distance covered = $70 \times 2 = 140$ km. * Remaining distance = $345 - 140 = 205$ km. 2. **Calculate Distance for Second Interval (Hours 3 & 4):** * Speed increases by $10$ km/hr. New speed = $80$ km/hr. Time = $2$ hours. * Distance covered = $80 \times 2 = 160$ km. * Remaining distance = $205 - 160 = 45$ km. 3. **Calculate Time for Remaining Distance (Hour 5+):** * Speed increases by $10$ km/hr again. New speed = $90$ km/hr. * Distance to cover = $45$ km. * Time required = $\frac{Distance}{Speed} = \frac{45}{90} = \frac{1}{2}$ hour. 4. **Calculate Total Time:** * Total Time = $2$ hours (first interval) + $2$ hours (second interval) + $\frac{1}{2}$ hour. * Total Time = $4\frac{1}{2}$ hours. ### Exam Strategy & Shortcut Maintain a running tally of distance and time: $2$ hrs -> $140$ km $4$ hrs -> $140 + 160 = 300$ km Need $45$ km more. Next speed is $90$ km/h. $45$ is exactly half of $90$, so it takes $0.5$ hours. $4 + 0.5 = 4.5$ hours. ### Common Pitfall Assuming the speed increases continuously (like continuous acceleration) rather than in stepped blocks every two hours. Using arithmetic progression formulas for continuous acceleration will yield an incorrect time. ### Final Answer Therefore, the correct answer is **$4\frac{1}{2}$ hrs**.