Question

Points A and B are 150 km apart. Cars 1 and 2 travel from A to B, but car 2 starts from A when car 1 is already 20 km away from A. Each car travels at a speed of 100 kmph for the first 50 km, at 50 kmph for the next 50 km, and at 25 kmph for the last 50 km. The distance, in km, between car 2 and B when car 1 reaches B is

Answer 1

Correct Answer: 5

Scenario: A car travels 150 km in three segments with different speeds, and we want to determine how far it is from point B at a specific time.

Step 1: Time Taken for Each Segment

• First 50 km at 100 km/hr:

\[ \text{Time} = \frac{50}{100} = \frac{1}{2} \text{ hr} \]

• Second 50 km at 50 km/hr:

\[ \text{Time} = \frac{50}{50} = 1 \text{ hr} \]

• Last 50 km at 25 km/hr:

\[ \text{Time} = \frac{50}{25} = 2 \text{ hr} \]

Total time taken by Car 1 for full 150 km:

\[ \frac{1}{2} + 1 + 2 = 3.5 \text{ hours} = 3 \text{ hr } 30 \text{ min} \]

Step 2: Car 1 Has Already Covered 20 km When Car 2 Starts

At 100 km/hr, time to cover 20 km:

\[ \frac{20}{100} = 0.2 \text{ hr } = 12 \text{ min} \]

So, after car 2 starts, time left for car 1 to reach B:

\[ 3 \text{ hr } 30 \text{ min } - 12 \text{ min } = 3 \text{ hr } 18 \text{ min } = 3.3 \text{ hr} \]

Step 3: Distance Covered in 3 hr 18 min

Breakdown of total distance traveled by car 1:

• First 50 km – already done
• Second 50 km – done at 50 km/hr → takes 1 hr
• In remaining 2 hr 18 min, it travels at 25 km/hr:

Remaining time for last segment:

\[ 3.3 - 1.5 = 1.8 \text{ hr } \quad \text{(1 hr from second segment + 0.5 hr from first)} \]

Time spent in third segment = 1.8 hr

Distance covered in 1.8 hr at 25 km/hr:

\[ 25 \times 1.8 = 45 \text{ km} \]

Step 4: Total Distance Covered by Car 1

\[ 50 + 50 + 45 = 145 \text{ km} \]

Step 5: Distance from Point B

\[ 150 - 145 = \boxed{5 \text{ km}} \]

Final Answer:

\[ \boxed{5 \text{ km from B}} \]