Answer and explanation:
a) To find the average speed of Miss Lim for the whole journey, we need to use the formula:
Average speed = Total distance ÷ Total time
Let's first calculate the total distance traveled by both Miss Wan and Miss Lim. We know that Miss Wan drove at an average speed of 60 km/h and reached Orchard Road 30 minutes later. So, the total distance traveled by her would be:
Distance = Speed × Time
Distance = 60 km/h × (30/60) h
Distance = 30 km
Now, we also know that Miss Lim was still 5 km away from Orchard Road when Miss Wan reached there. Therefore, the total distance traveled by both of them would be:
Total distance = Distance covered by Miss Wan + Distance left for Miss Lim
Total distance = 30 km + 5 km
Total distance = 35 km
Next, let's calculate the total time taken by both of them. We know that Miss Wan took 30 minutes less than Miss Lim to reach Orchard Road. So, if we assume that Miss Lim took t hours to reach Orchard Road, then Miss Wan took (t - 0.5) hours. Therefore, the total time taken by both of them would be:
Total time = Time taken by Miss Wan + Time taken by Miss Lim
Total time = (t - 0.5) h + t h
Total time = 2t - 0.5 h
Now, we can use the formula to find the average speed of Miss Lim:
Average speed = Total distance ÷ Total time
Average speed = 35 km ÷ (2t - 0.5) h
Therefore, the average speed of Miss Lim for the whole journey is 35/(2t-0.5) km/h.
b) To find out what time Miss Lim would reach Orchard Road, we can use the formula:
Time taken = Distance ÷ Speed
We know that Miss Lim was 5 km away from Orchard Road when Miss Wan reached there. Therefore, the distance left for Miss Lim to cover would be:
Distance = 5 km
We also know that Miss Lim's average speed for the whole journey is 35/(2t-0.5) km/h. Therefore, the time taken by her to cover the remaining distance of 5 km would be:
Time taken = Distance ÷ Speed
Time taken = 5 km ÷ 35/(2t-0.5) km/h
Time taken = (2t - 0.5) ÷ 7 h
Now, we need to add this time to the time when Miss Wan reached Orchard Road, which was 30 minutes past 2.50 p.m. So, the time when Miss Lim would reach Orchard Road would be:
Time = Time when Miss Wan reached Orchard Road + Time taken by Miss Lim
Time = 2.50 p.m. + 30 min + (2t - 0.5) ÷ 7 h
Simplifying this equation, we get:
Time = (14t + 11) ÷ 14 p.m.
Therefore, Miss Lim would reach Orchard Road at (14t + 11) ÷ 14 p.m.