The speeds of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination?

### Concept & Ratios in Kinematics When distance is constant, the ratio of times taken by two bodies is the inverse of the ratio of their speeds. ### Step-by-Step Solution * **Set up Ratios:** The ratio of speeds of A and B is $3 : 4$. * Therefore, the ratio of time taken by A and B is $4 : 3$. * **Assign Variables:** Let the time taken by A be $4x$ and by B be $3x$. * **Use Given Condition:** A takes 20 minutes more than B. So, $4x - 3x = 20$, which means $x = 20$. * **Calculate A's Time:** Time taken by A = $4x = 4 \times 20 = 80$ minutes. * **Format Answer:** 80 minutes is equal to $1$ hour and $20$ minutes, or $1\frac{20}{60} = 1\frac{1}{3}$ hours. ### Exam Strategy & Shortcut Notice the gap in the time ratio parts: A takes 4 parts of time, B takes 3 parts. The difference is 1 part. We are given this 1 part difference is exactly 20 minutes. Therefore, A's time (4 parts) is simply $4 \times 20 = 80$ minutes without formal algebra. ### Common Pitfall Solving for $x$ correctly but mistakenly calculating the time for B (60 minutes) instead of A, or botching the conversion from 80 minutes into a mixed fractional hour. ### Final Answer Therefore, the correct answer is **$1\frac{1}{3}$ hours**.