Subjects algebra

Bus Time Squares

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Bus Time Squares


1. **Problem statement:** A bus took 20% more time due to a traffic jam and the journey took 150 minutes. If the bus reached Town B at 10:25 hours, find the departure time from Town A. 2. Let the normal time to travel be $t$ minutes. Given the time taken with traffic jam is $t + 0.20t = 1.20t$. 3. We know $1.20t = 150$ minutes. Solve for $t$: $$t = \frac{150}{1.20} = 125 \text{ minutes}$$ 4. The bus took 150 minutes and reached at 10:25. To find the departure time, subtract 150 minutes (2 hours 30 minutes) from 10:25: $$10:25 - 2:30 = 7:55$$ So, the bus left Town A at 7:55 hours. 5. **Answer for (a):** 7:55 hours. --- 6. **Problem statement:** Find the travel time if there was no traffic jam. 7. From step 3, normal travel time $t = 125$ minutes. 8. **Answer for (b):** 125 minutes. --- 9. **Problem statement:** Diagrams formed by squares. (a) Drawing diagram 4 is a visual task; cannot provide textual drawing here. (b) We need to find the number of squares in diagram 8. 10. Observing the pattern of squares: Diagram 1 has 4 squares. Diagram 2 has 6 squares. Diagram 3 has 9 squares. 11. Notice the pattern of square counts: 4, 6, 9. Let's hypothesize that the number of squares in Diagram $n$ follows a certain sequence. 12. Diagram 1: 2x2 grid minus 0 = 4 squares Diagram 2: 2x3 grid minus 0 = 6 squares Diagram 3: 3x3 grid = 9 squares It appears that Diagram $n$ has $n \times n$ squares or similar arrangement increasing approximately as square numbers or close. 13. Since Diagram 3 has $9$ squares ($3^2$), Diagram 8 likely has $8^2 = 64$ squares. 14. **Answer for (b):** 64 squares. --- 15. **Problem statement:** Which diagram has 27 squares? 16. Since 27 is $3^3$, but squares are counted usually in two dimensions, likely the diagram with $27$ squares corresponds to Diagram 5 or possibly Diagram 3x3x3 arrangement. 17. Given the pattern, Diagram 3 has 9 squares, so Diagram 5 should have $5^2 = 25$ squares approximately, which is not 27. 18. Hence, the diagram with 27 squares is diagram 6 or adapted. But likely the diagram with $27$ squares is Diagram 3D cube of $3 \times 3 \times 3$ cubes. 19. But since the question asks about the diagrams formed by squares (2D), the one with 27 squares is Diagram 3 (9 squares), or the question refers to a cube-like figure which is not given. 20. Alternatively, if the question refers to Diagram 3, which has 9 squares, then the diagram with 27 squares would be Diagram 5 or extended. 21. Assuming the identification from the problem, the diagram with 27 squares is Diagram 3 (3x3 grid) multiplied or stacked, but since this info is ambiguous, answer is Diagram 3. 22. **Answer for (c):** Diagram 3.