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# Michael walks at the rate of 5 feet per second on a long straight path

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Michael walks at the rate of 5 feet per second on a long straight path  [#permalink]

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27 Mar 2019, 22:19
00:00

Difficulty:

65% (hard)

Question Stats:

27% (01:53) correct 73% (03:30) wrong based on 15 sessions

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Michael walks at the rate of 5 feet per second on a long straight path. Trash pails are located every 200 feet along the path. A garbage truck traveling at 10 feet per second in the same direction as Michael stops for 30 seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leaving the next pail. How many times will Michael and the truck intersect?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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Re: Michael walks at the rate of 5 feet per second on a long straight path  [#permalink]

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28 Mar 2019, 02:45
Bunuel wrote:
Michael walks at the rate of 5 feet per second on a long straight path. Trash pails are located every 200 feet along the path. A garbage truck traveling at 10 feet per second in the same direction as Michael stops for 30 seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leaving the next pail. How many times will Michael and the truck intersect?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Michael Speed = 5 ft / sec
Garbage truck speed = 10 ft/sec

Time that Michael takes to reach one pail from the other = 200/5 = 40 secs
Time that Garbage truck takes to reach one pail from the other = 200/10 = 20 secs

Garbage truck reached the second pails at the following time intervals - 20 sec to 50 seconds
Garbage truck at third Pail will be available at time interval 70 sec to 100 secs
Garbage truck at forth Pail will be available at time interval 120 sec to 150 secs
Garbage truck at fifth Pail will be available at time interval 170 sec to 200 secs and so on

Michael will reach at second pail at 40th sec i.e. It intersects with the truck
Michael will reach at third pail at 80th sec i.e. It intersects with the truck
Michael will reach at Forth pail at 120th sec i.e. It intersects with the truck
Michael will reach at Fifth pail at 160th sec i.e. It DOES NOT intersects with the truck

Since they also intersect at the first pail so total points of intersections = 4

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Michael walks at the rate of 5 feet per second on a long straight path  [#permalink]

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Updated on: 28 Mar 2019, 12:01
Bunuel wrote:
Michael walks at the rate of 5 feet per second on a long straight path. Trash pails are located every 200 feet along the path. A garbage truck traveling at 10 feet per second in the same direction as Michael stops for 30 seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leaving the next pail. How many times will Michael and the truck intersect?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

time taken by truck = 200/10 ; 20 sec
time taken by Michae; 200/5; 40 seconds
key catch of question +30 seconds halt at each pail

so first stop ; 0 to 20 sec truck moves at 20+30 ; 50 seconds
2nd stop ; 70 sec ; move at 70+30 ; 100 sec
3rd stop; 120 sec ; move at 150 sec
4th stop; 170 ; move 200 sec
5th stop; 220 sec ; move 250 sec
6th; 270; move 300 sec
for Michael
1st stop; 40 sec
2nd; 80 sec
3rd; 120 sec
4th; 160 sec
5th ; 200 sec
6th; 240 sec
so we see that until 5th stop both truck and Michael are meeting each other; but at 6th stop Truck overtakes Michael and they dont meet any further
IMO B; 5
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Originally posted by Archit3110 on 28 Mar 2019, 03:47.
Last edited by Archit3110 on 28 Mar 2019, 12:01, edited 1 time in total.
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Posts: 58
Location: India
Michael walks at the rate of 5 feet per second on a long straight path  [#permalink]

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28 Mar 2019, 09:53
Bunuel wrote:
Michael walks at the rate of 5 feet per second on a long straight path. Trash pails are located every 200 feet along the path. A garbage truck traveling at 10 feet per second in the same direction as Michael stops for 30 seconds at each pail. As Michael passes a pail, he notices the truck ahead of him just leaving the next pail. How many times will Michael and the truck intersect?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

IMO ans should be B (5 times).

Explanation:
Distance between two pails: 200 ft
Michael's speed: 5 ft/s ---> He will take 40 secs to reach from one pail to another
Truck's speed: 10 ft/s ---> It will take 20 secs to reach from one pail to another
Waiting time for garbage truck in each pail : 30 secs

Suppose Michael starts from pail A and as given the garbage truck starts from pail B.
Michael will take 40 secs to reach B and in the same time Truck will reach C and wait for 20 secs (20+20 secs wait at C).
In the next 40 secs, Michael will go from B to C, and Truck will go from C to D (10 secs wait at C+20 secs travel+10 secs wait at D).
In the next 40 secs, Michael will go from C to D, and Truck will just reach E from D (20 secs waiting at D+20 secs travel).
In the next 40 secs, Michael will go from D to E, and Truck will be midway from E to F (30 secs waiting at E +10 secs travel).
In the next 40 secs, Michael will go from E to F, and Truck will be just starting from F (10 secs travel +30 secs waiting at F) ----------1st intersect
In the next 40 secs, Michael will go from F to G, and Truck will go from F to G (20 secs travel+20 secs waiting at G) . -------------------2nd intersect
In the next 40 secs, Michael will go from G to H, and Truck will go from G to H (10 secs waiting at G + 20 secs travel+ 10 secs waiting at H)
------Here there are two intersects: One while traveling from G to H, Truck crossed Michael and after reaching H, Michael intersected the truck. -------------------3rd and 4th intersect
In the next 40 secs, Michael will go from H to I, and Truck will go from H to I (20 secs waiting at H and 20 secs travel) -------5th intersect

And after this point the truck will always move ahead to Michael and never intersect. Please do let me know if the explanation is correct or not. Thanks.
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Re: Michael walks at the rate of 5 feet per second on a long straight path  [#permalink]

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30 Mar 2019, 10:09
A very interesting problem indeed!

P1____________P2___m1_________P3______m2______P4_________m3___P5____________ P6 ____________P7___m5___i3______P8______m6______P9
(m4/i1) (i2) (i4) (i5)
P9_________m7___P10

I had to make the explanation quite lengthy – maybe unnecessarily so – but I did so to make the concept absolutely clear to remove any confusion.
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Posts: 70
Re: Michael walks at the rate of 5 feet per second on a long straight path  [#permalink]

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30 Mar 2019, 12:25
Sorry, the diagram got a bit messed up in the copy-paste process. I have modified it slightly; hope it is clear now.

P1____________P2___m1_________P3______m2______P4_________m3___P5____________ P6/(m4/i1)
____________P7/i2___m5___i3______P8/i4______m6______P9/i5_________m7___P10
Re: Michael walks at the rate of 5 feet per second on a long straight path   [#permalink] 30 Mar 2019, 12:25
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