Solution
Given:• Gunther delivered pizzas in three different societies – Hufflepuff, Ravenclaw, and Slytherin
• He started his journey at 6:30 pm from the shop at a speed of 15 mph
• In 15 minutes, he reached Hufflepuff society and took 15 minutes to deliver all pizzas in that society
• He again travelled for another 15 minutes to reach Ravenclaw society at the same speed of 15 minutes
• At Ravenclaw society, he took 15 minutes to deliver all pizzas in that society
• He again travelled for another 15 minutes to reach Slytherin society, at double of original speed, i.e. 30 mph
• After reaching Slytherin society he found out that the order was cancelled in that society
To find:• Gunther’s average speed in this whole journey (time includes delivery time)
Approach and Working: All the information can be shown in the following table:
• As the journey is divided into three separate parts, let us calculate the journey distance first.
o From the shop to Hufflepuff society, Gunther travelled for 15 minutes at 15 mph
Therefore, the distance covered = \(\frac{15}{60}\) * 15 miles = \(\frac{15}{4}\) miles
o From Hufflepuff society to Ravenclaw society, Gunther travelled for 15 minutes at 15 mph
Therefore, the distance covered = \(\frac{15}{60}\) * 15 miles = \(\frac{15}{4}\) miles
o From Ravenclaw society to Slytherin society, Gunther travelled for 15 minutes at 30 mph
Therefore, the distance covered = \(\frac{30}{60}\) * 15 miles = \(\frac{15}{2}\) miles
o Hence, the total distance covered = (\(\frac{15}{4} + \frac{15}{4} + \frac{15}{2}\)) miles = \(\frac{60}{4}\) miles = 15 miles
• Now, let’s calculate the total journey time
o From the shop to the delivery at Hufflepuff society, Gunther travelled for 15 minutes and delivered pizzas for 15 minutes
Therefore, the total time taken = (15 + 15) = 30 minutes
o From Hufflepuff society to the delivery at Ravenclaw society, Gunther travelled for 15 minutes and delivered pizzas for 15 minutes
Therefore, the total time taken = (15 + 15) = 30 minutes
o From Ravenclaw society to Slytherin society, Gunther travelled for 15 minutes only
Therefore, the total time taken = 15 minutes
o Hence, the total time taken in the whole journey = (30 + 30 + 15) minutes = 75 minutes
• As we already know the total distance travelled and the total journey time, we can say the average speed = total distance travelled/total time taken = \(\frac{15}{75}\) miles per minutes = \(\frac{1}{5}\) miles per minute = \(\frac{1}{5}\) * 60 mph = 12 mph
Hence, the correct answer is option C.
Answer: C _________________