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While Steve and LeRoy are fishing 1 mile from shore, their boat spring

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Math Expert
Joined: 02 Sep 2009
Posts: 58396
While Steve and LeRoy are fishing 1 mile from shore, their boat spring  [#permalink]

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27 Mar 2019, 00:13
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Difficulty:

55% (hard)

Question Stats:

66% (02:33) correct 34% (02:38) wrong based on 50 sessions

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While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

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Joined: 27 Sep 2018
Posts: 37
Re: While Steve and LeRoy are fishing 1 mile from shore, their boat spring  [#permalink]

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27 Mar 2019, 00:43
2
time taken to reach shore= Distance/speed= 1/4*60=15 min

Water that will fill in the boat in 15 mins at constant rate of 10 gallons /minute= 150 gallons

water boat can hold without sinking = 30 gallons

water tp be taken out= 150-30= 120 gallons

rate at which water is to be taken out = total water/ tim eto reach shore=120/15= 8 gallons / min
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Re: While Steve and LeRoy are fishing 1 mile from shore, their boat spring  [#permalink]

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27 Mar 2019, 03:15
Bunuel wrote:
While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

total time to reach back shore = 1/4 * 60 = 15 mins
and 30 gallons of water boat can take ; ie it would be filled in by 30/15 ; 2 gallons per mins
rate inflow = 10 gpm
so rate for GPM = 10-2 ; 8 gpm
IMO D
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Re: While Steve and LeRoy are fishing 1 mile from shore, their boat spring  [#permalink]

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29 Mar 2019, 07:35
Bunuel wrote:
While Steve and LeRoy are fishing 1 mile from shore, their boat springs a leak, and water comes in at a constant rate of 10 gallons per minute. The boat will sink if it takes in more than 30 gallons of water. Steve starts rowing toward the shore at a constant rate of 4 miles per hour while LeRoy bails water out of the boat. What is the slowest rate, in gallons per minute, at which LeRoy can bail if they are to reach the shore without sinking?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

It takes them 1/4 hours = 15 minutes to reach the shore.

Let n = the number of gallons per minute that LeRoy can bail water out of the boat and still arrive at the shore in 15 minutes with 30 gallons of water. Thus:

(10 - n) x 15 = 30

10 - n = 2

8 = n

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Re: While Steve and LeRoy are fishing 1 mile from shore, their boat spring   [#permalink] 29 Mar 2019, 07:35
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