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Challenge question: At noon, Joe and a hummingbird leave

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Challenge question: At noon, Joe and a hummingbird leave

by Brent@GMATPrepNow » Sat Oct 27, 2018 10:33 am

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At noon, Joe and a hummingbird leave point A and travel towards point B, which is 12 miles away. At the same time Sue leaves point B and travels toward point A. Joe, Sue and the hummingbird travel at constant speeds of 3 miles per hour, 4 miles per hour, and 84 miles per hour respectively. When the hummingbird reaches Sue, it immediately changes direction and heads toward Joe. When it reaches Joe, it turns around and heads toward Sue. If this process continues until Sue and Joe meet, what is the total distance traveled by the hummingbird?

A) 49 miles
B) 84 miles
C) 121 miles
D) 144 miles
E) 168 miles

Answer: D
Difficulty level: 700+
Source: www.gmatprepnow.com
Brent Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Sun Oct 28, 2018 2:19 pm
Brent@GMATPrepNow wrote:At noon, Joe and a hummingbird leave point A and travel towards point B, which is 12 miles away. At the same time Sue leaves point B and travels toward point A. Joe, Sue and the hummingbird travel at constant speeds of 3 miles per hour, 4 miles per hour, and 84 miles per hour respectively. When the hummingbird reaches Sue, it immediately changes direction and heads toward Joe. When it reaches Joe, it turns around and heads toward Sue. If this process continues until Sue and Joe meet, what is the total distance traveled by the hummingbird?

A) 49 miles
B) 84 miles
C) 121 miles
D) 144 miles
E) 168 miles

Answer: D
Difficulty level: 700+
Source: www.gmatprepnow.com
The main idea here is that all 3 travelers travel for the SAME amount of time.

So, let's first determine the time it takes for Joe and Sue to meet.
This is a shrinking gap question.

To determine the rate at which the gap shrinks, we'll ADD the travel speeds of Joe and Sue
That is, shrink rate = (3 miles per hour) + (4 miles per hour) = 7 miles per hour

At noon, the gap between Joe and Sue is 12 miles.
time = distance/speed
So, the time it takes to reduce the gap to zero = 12/7
That is, it takes 12/7 hours until Joe and Sue meet.

During those 12/7 hours, the hummingbird is flying at a constant speed of 84 mph
distance = (speed)(time)
So, the distance traveled by the hummingbird = (84)(12/7) = 144 miles

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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