Gunther, the pizza delivery boy, went out from the store

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BTGmoderatorLU: Moderator; Posts: 2598; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Sep 14, 2018 6:41 pm

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Source: e-GMAT

Gunther, the pizza delivery boy, went out from the store carrying pizzas to deliver for the residents in 3 housing societies named Hufflepuff, Ravenclaw, and Slytherin. He started at 6:30 pm from the shop at a speed of 15 mph. After 15 minutes he reached Hufflepuff Society, and it took 15 minutes to deliver all pizzas there. Then at the same speed he moved for another 15 minutes to reach Ravenclaw, and in 15 minutes delivered all pizza. Finally, he drove towards Slytherin at double of his original speed, and after reaching there in 15 minutes time, he realised that the order has been cancelled. What is Gunther's average speed in this whole journey (time includes delivery time)?

A. 8 mph
B. 10 mph
C. 12 mph
D. 15 mph
E. 30 mph

The OA is C.

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Source: Beat The GMAT — Problem Solving | Fri Sep 14, 2018 6:41 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Fri Sep 14, 2018 7:49 pm

BTGmoderatorLU wrote:Source: e-GMAT

Gunther, the pizza delivery boy, went out from the store carrying pizzas to deliver for the residents in 3 housing societies named Hufflepuff, Ravenclaw, and Slytherin. He started at 6:30 pm from the shop at a speed of 15 mph. After 15 minutes he reached Hufflepuff Society, and it took 15 minutes to deliver all pizzas there. Then at the same speed he moved for another 15 minutes to reach Ravenclaw, and in 15 minutes delivered all pizza. Finally, he drove towards Slytherin at double of his original speed, and after reaching there in 15 minutes time, he realised that the order has been cancelled. What is Gunther's average speed in this whole journey (time includes delivery time)?

A. 8 mph
B. 10 mph
C. 12 mph
D. 15 mph
E. 30 mph

The OA is C.

> Time taken to reach Hufflepuff Society = 15 minutes
> Time taken to deliver Pizzas at Hufflepuff Society = 15 minutes
> Time taken to reach Ravenclaw Society = 15 minutes
> Time taken to deliver Pizzas at Ravenclaw Society = 15 minutes
> Time taken to reach Slytherin Society = 15 minutes

Total time taken = 5 * 15 = 75 minutes = 1.25 hours

> Distance traveled to reach Hufflepuff Society driving @ 15 mph for 15 minutes = 15/4 miles
> Distance traveled to reach Ravenclaw Society driving @ 15 mph for 15 minutes = 15/4 miles
> Distance traveled to reach Slytherin Society driving @ 30 mph for 15 minutes = 15/2 miles

Total distance travelled = 15/4 + 15/4 + 15/2 = 15 miles

Average speed = Total distance traveled / Total time taken = 15 / 1.25 = 12 mph

The correct answer: C

Hope this helps!

-Jay
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Sep 15, 2018 1:55 am

BTGmoderatorLU wrote:Source: e-GMAT

Gunther, the pizza delivery boy, went out from the store carrying pizzas to deliver for the residents in 3 housing societies named Hufflepuff, Ravenclaw, and Slytherin. He started at 6:30 pm from the shop at a speed of 15 mph. After 15 minutes he reached Hufflepuff Society, and it took 15 minutes to deliver all pizzas there. Then at the same speed he moved for another 15 minutes to reach Ravenclaw, and in 15 minutes delivered all pizza. Finally, he drove towards Slytherin at double of his original speed, and after reaching there in 15 minutes time, he realised that the order has been cancelled. What is Gunther's average speed in this whole journey (time includes delivery time)?

A. 8 mph
B. 10 mph
C. 12 mph
D. 15 mph
E. 30 mph

Average = sum/quantity.
In this case:
Average speed = (sum of the minutes spent at each speed)/(total number of minutes).

Total time spent at 15mph = 30 minutes.
Total time spent delivering pizzas at 0mph = 30 minutes.
Total time spent at 30mph = 15 minutes.
Average speed = (15*30 + 0*30 + 30*15)/(30 + 30 + 15) = 900/75 = 300/25 = 60/5 = 12.

The correct answer is C.

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