Question

In a 700 m race, Amit reaches the finish point in 20 seconds and Rahul reaches in 25 seconds. Amit beats Rahul by a distance of:

• A. 120 m
• B. 150 m
• C. 140 m
• D. 100 m

Hint:

When comparing the performance of two competitors in a race or any timed activity, always start by calculating their individual speeds using the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \). Once you have their speeds, you can compute the distance each person covers in the same amount of time. This allows you to directly compare their performances and calculate the difference in distance. In this problem, after calculating each person's speed, we found how far Rahul had traveled in the same time Amit finished the race and then computed the distance by which Amit beats Rahul.

Answer 1

The Correct Option is C

Amit completes the race in 20 seconds, so his speed is:

Speed of Amit = \( \frac{\text{Distance}}{\text{Time}} = \frac{700}{20} = 35 \, \text{m/s} \).

Rahul completes the race in 25 seconds, so his speed is:

Speed of Rahul = \( \frac{\text{Distance}}{\text{Time}} = \frac{700}{25} = 28 \, \text{m/s} \).

In 20 seconds, Rahul covers:

Distance covered by Rahul = Speed of Rahul \(\times\) Time = \( 28 \times 20 = 560 \, \text{m} \).

The distance by which Amit beats Rahul is:

Distance = \( 700 - 560 = 140 \, \text{m} \).

Thus, Amit beats Rahul by 140 m.

Answer 2

Amit completes the race in 20 seconds, so his speed is:

To calculate Amit's speed, we use the fundamental formula for speed: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] Amit completes the race of 700 meters in 20 seconds. Substituting these values into the formula, we get: \[ \text{Speed of Amit} = \frac{700}{20} = 35 \, \text{m/s}. \] This means Amit's speed is 35 meters per second, which is how fast he completes the race.

Rahul completes the race in 25 seconds, so his speed is:

Rahul completes the same 700-meter race, but in 25 seconds. Using the same formula for speed: \[ \text{Speed of Rahul} = \frac{700}{25} = 28 \, \text{m/s}. \] So, Rahul's speed is 28 meters per second, which is slower than Amit's speed by 7 meters per second.

In 20 seconds, Rahul covers:

Now, to compare how far Rahul has traveled when Amit finishes the race in 20 seconds, we use Rahul's speed and the time Amit took to complete the race: \[ \text{Distance covered by Rahul} = \text{Speed of Rahul} \times \text{Time} = 28 \times 20 = 560 \, \text{m}. \] This means in the 20 seconds that Amit takes to complete the race, Rahul manages to cover 560 meters.

The distance by which Amit beats Rahul is:

To find the distance by which Amit beats Rahul, we subtract the distance Rahul covers from the total race distance (700 meters): \[ \text{Distance} = 700 - 560 = 140 \, \text{m}. \] Therefore, Amit beats Rahul by 140 meters, meaning if Rahul had continued at his pace, it would take him another 140 meters to finish the race.

Conclusion: Thus, Amit beats Rahul by 140 m. Amit's faster speed enables him to cover the race in less time, leaving Rahul behind by a considerable distance.