A can run a distance in 30 minutes, while B can run the same distance in 45 minu

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Question: A can run a distance in 30 minutes, while B can run the same distance in 45 minutes. What is the ratio of their speeds?

Options:

Correct Answer: 3:2

Solution:

Speed is inversely proportional to time. Ratio of speeds = 45:30 = 3:2.

A can run a distance in 30 minutes, while B can run the same distance in 45 minutes. What is the ratio of their speeds?

A can run a distance in 30 minutes, while B can run the same distance in 45 minutes. What is the ratio of their speeds?

Step 1: Understand that speed is calculated as distance divided by time.
Step 2: Since both A and B run the same distance, we can compare their speeds based on the time they take.
Step 3: A takes 30 minutes to run the distance, so we can say A's speed is 1/30.
Step 4: B takes 45 minutes to run the same distance, so B's speed is 1/45.
Step 5: To find the ratio of their speeds, we compare 1/30 and 1/45.
Step 6: To compare these fractions, we can find a common denominator or simply take the inverse of the times.
Step 7: The ratio of their speeds is the inverse of the ratio of their times: 45 (B's time) to 30 (A's time).
Step 8: Simplify the ratio 45:30 by dividing both numbers by 15, which gives us 3:2.

Speed and Time Relationship – Speed is calculated as distance divided by time, and when comparing two speeds, the ratio can be derived from their respective times.
Ratio Simplification – Understanding how to simplify ratios correctly is crucial for arriving at the correct answer.