SOLUTION: Rahul is sailing at a uniform speed when a leak develops in his boat. He uses a bucket to empty water from the boat and reaches the shore in 30 minutes just in time to avoid sinkin

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Question 844043: Rahul is sailing at a uniform speed when a leak develops in his boat. He uses a bucket to empty water from the boat and reaches the shore in 30 minutes just in time to avoid sinking. The leak fills the boat twice as fast as the Rahul is able to empty it. Had the leak developed 10 minutes earlier how much faster would the Rahul have had to work to reach the shore safely?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Rahul is sailing at a uniform speed when a leak develops in his boat.
He uses a bucket to empty water from the boat and reaches the shore in 30 minutes just in time to avoid sinking.
The leak fills the boat twice as fast as the Rahul is able to empty it.
Had the leak developed 10 minutes earlier how much faster would the Rahul have had to work to reach the shore safely?
:
Let r = rate of removing water from the boat
then
2r = rate of water leaking into the boat
:
let a boat full of water, ready to sink = 1
:
30%2Fr - 30%2F%282r%29 = 1
2(30) - 30 = 2r
60 - 30 = 2r
30 = 2r
r = 15 rate of removing water from the boat
:
Find the rate if leak occurs 10 min earlier (40 min to the shore)
40%2Fr - 40%2F%282r%29 = 1
2(40) - 40 = 2r
2r = 40
r = 20 rate of removing water from the boat
I guess you could say remove the water; 5/15 = 33% faster