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At noon, Joe and a hummingbird leave Point A and travel towards point

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CEO
Joined: 12 Sep 2015
Posts: 3722
At noon, Joe and a hummingbird leave Point A and travel towards point  [#permalink]

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27 Oct 2018, 11:36
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8
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Difficulty:

35% (medium)

Question Stats:

79% (02:25) correct 21% (02:26) wrong based on 44 sessions

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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

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Manager
Joined: 09 Oct 2015
Posts: 237
Re: At noon, Joe and a hummingbird leave Point A and travel towards point  [#permalink]

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27 Oct 2018, 11:52
1
Is it d?
The bird would fly continously until the 2 people meet. The time for the 2 people to meet is 12/7
Dist travelled by bird = 12/7 x 84

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CEO
Joined: 12 Sep 2015
Posts: 3722
Re: At noon, Joe and a hummingbird leave Point A and travel towards point  [#permalink]

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28 Oct 2018, 15:23
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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

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

Cheers,
Brent
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Re: At noon, Joe and a hummingbird leave Point A and travel towards point   [#permalink] 28 Oct 2018, 15:23
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