The ratio of speeds of A:B is 1:4. If B covers a distance in 20 min, A will cover it inA)77 minutesB)67 minutesC)70 mimutesD)None of these.

1. Break Down the Problem

To find how long it takes for A to cover the same distance that B covers in 20 minutes, we need to use the given speed ratio and relate their speeds to the time taken.

Let:

• Speed of A = $v_A$
• Speed of B = $v_B$

Given the ratio is $\frac{v_A}{v_B} = \frac{1}{4}$. Therefore, we can express the speed of B in terms of A:

• $v_B = 4v_A$

2. Relevant Concepts

Using the relationship between speed, distance, and time: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ From this, we derive: $\text{Distance} = \text{Speed} \times \text{Time}$

3. Analysis and Detail

• Let the distance covered by B in 20 minutes be $D$. $D = v_B \times 20 \text{ minutes}$
• Since $v_B = 4v_A$, substituting gives: $D = 4v_A \times 20$
• Now, A's time to cover the same distance $D$: $D = v_A \times t_A$ Setting the two expressions for $D$ equal: $4v_A \times 20 = v_A \times t_A$
• Dividing both sides by $v_A$ (assuming $v_A \neq 0$): $80 = t_A$

4. Verify and Summarize

Thus, the time taken by A to cover the same distance is 80 minutes. However, we are looking at the choices given in the question.

Final Answer

The final answer is D) None of these. A will cover the distance in 80 minutes, which is not listed among the options provided.