A can run a distance in 30 minutes. If he increases his speed by 50%, how much t

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Question: A can run a distance in 30 minutes. If he increases his speed by 50%, how much time will he take to cover the same distance?

Options:

Correct Answer: 20 minutes

Solution:

If speed increases by 50%, time decreases by 1/(1 + 0.5) = 2/3. Time taken = 30 minutes * 2/3 = 20 minutes.

A can run a distance in 30 minutes. If he increases his speed by 50%, how much time will he take to cover the same distance?

A can run a distance in 30 minutes. If he increases his speed by 50%, how much time will he take to cover the same distance?

Step 1: Understand that A can run a distance in 30 minutes.
Step 2: Calculate A's original speed. Speed = Distance / Time. Let the distance be D. So, Speed = D / 30 minutes.
Step 3: A increases his speed by 50%. This means his new speed = Original Speed + 50% of Original Speed.
Step 4: Calculate the new speed. New Speed = (D / 30) + 0.5 * (D / 30) = (D / 30) * (1 + 0.5) = (D / 30) * (1.5).
Step 5: Simplify the new speed. New Speed = (1.5D) / 30 = D / 20.
Step 6: Now, calculate the time taken to cover the same distance D with the new speed. Time = Distance / New Speed = D / (D / 20).
Step 7: Simplify the time calculation. Time = D * (20 / D) = 20 minutes.
Step 8: Conclusion: If A increases his speed by 50%, he will take 20 minutes to cover the same distance.

Speed and Time Relationship – Understanding the inverse relationship between speed and time, where increasing speed results in decreased time to cover the same distance.
Percentage Increase – Calculating the new speed after a percentage increase and its effect on time taken.