A certain motor car starts at the speed of 70 km/hr. It accelerates, increasing its speed every two hours by an amount of 10 km/h. What is the time it will take to cover a distance of 345 km?

Options

A. a. 2 (1/4) hrs
B. b. 4 hrs 5 min
C. c. 4 (1/2) hrs
D. d. Can't be determined

Answer

To solve the problem step by step, we will calculate the distance covered by the car over time and determine how long it takes to cover a total distance of 345 km.

### Step 1: Determine the initial speed and acceleration
The car starts with a speed of 70 km/h and increases its speed by 10 km/h every 2 hours.

### Step 2: Calculate the distance covered in the first 2 hours
- Speed during the first 2 hours = 70 km/h
- Distance covered in the first 2 hours = Speed × Time = 70 km/h × 2 h = 140 km

### Step 3: Calculate the speed and distance covered in the next 2 hours
After the first 2 hours, the speed increases by 10 km/h:
- New speed = 70 km/h + 10 km/h = 80 km/h
- Distance covered in the next 2 hours = Speed × Time = 80 km/h × 2 h = 160 km

### Step 4: Calculate the total distance covered after 4 hours
- Total distance after 4 hours = Distance from first 2 hours + Distance from second 2 hours
- Total distance = 140 km + 160 km = 300 km

### Step 5: Calculate the remaining distance to cover
- Total distance to cover = 345 km
- Distance already covered = 300 km
- Remaining distance = 345 km - 300 km = 45 km

### Step 6: Calculate the speed for the next segment
After 4 hours, the speed increases again by 10 km/h:
- New speed = 80 km/h + 10 km/h = 90 km/h

### Step 7: Calculate the time to cover the remaining distance
- Time to cover the remaining distance = Remaining distance / Speed
- Time = 45 km / 90 km/h = 0.5 hours

### Step 8: Calculate the total time taken
- Total time = Time for first 4 hours + Time for remaining distance
- Total time = 4 hours + 0.5 hours = 4.5 hours

### Final Answer
The total time taken to cover a distance of 345 km is **4.5 hours**.

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