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

Arithmetic

Time, Speed & Distance

Medium

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

Entered answer:

✅ Correct Answer: 5

Understanding the Problem Setup

Points A and B are 150 km apart. Both cars follow the same speed pattern:

First 50 km at 100 kmph

Next 50 km at 50 kmph

Last 50 km at 25 kmph

The key difference: Car 2 starts when Car 1 is already 20 km away from A.

Find the Time Head Start

When Car 1 has traveled 20 km, Car 2 starts its journey.

Since Car 1 travels the first 50 km at 100 kmph:

Time to travel 20 km $= \frac{\text{Distance}}{\text{Speed}} = \frac{20}{100} = 0.2$ hours $= 12$ minutes

So Car 1 has a 12-minute head start over Car 2.

Calculate Total Time for Car 1 to Reach B

Car 1's journey breakdown:

First 50 km at 100 kmph: Time $= \frac{50}{100} = 0.5$ hours

Next 50 km at 50 kmph: Time $= \frac{50}{50} = 1$ hour

Last 50 km at 25 kmph: Time $= \frac{50}{25} = 2$ hours

Total time for Car 1 $= 0.5 + 1 + 2 = 3.5$ hours

Find Car 2's Travel Time When Car 1 Reaches B

Since Car 2 started 12 minutes (0.2 hours) later:

Car 2's travel time $= 3.5 - 0.2 = 3.3$ hours

Calculate How Far Car 2 Travels in 3.3 Hours

Car 2's journey in 3.3 hours:

First 50 km at 100 kmph: Takes 0.5 hours

Next 50 km at 50 kmph: Takes 1 hour

Remaining time $= 3.3 - 0.5 - 1 = 1.8$ hours

In the last segment (25 kmph zone), Car 2 travels for 1.8 hours:

Distance covered $= \text{Speed} \times \text{Time} = 25 \times 1.8 = 45$ km

Total distance covered by Car 2 $= 50 + 50 + 45 = 145$ km

Find Distance Between Car 2 and B

Distance between Car 2 and B $= \text{Total distance} - \text{Distance covered by Car 2}$

$= 150 - 145 = 5$ km

Since both cars follow identical speed patterns, the time difference between them remains constant throughout their journey. Car 1's 12-minute head start means Car 2 will always be 12 minutes behind, which translates to being 5 km away from B when Car 1 reaches B.

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