SOLUTION: Can someone please help me solve this word problem. I'm studying on Fractional Equations and Problem Solving. Thank you! In a survivor competition, the Pachena tribe can shuck

Question 607978: Can someone please help me solve this word problem. I'm studying on Fractional Equations and Problem Solving. Thank you!
In a survivor competition, the Pachena tribe can shuck 300 oysters in 10 minutes less time than it takes the Tchaika tribe. If the Pachena tribe shucks oysters at a rate of 5 oysters per minute faster than the Tchaika tribe, find the rate of each tribe.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In a survivor competition, the Pachena tribe can shuck 300 oysters in 10 minutes less time than it takes the Tchaika tribe.
If the Pachena tribe shucks oysters at a rate of 5 oysters per minute faster than the Tchaika tribe, find the rate of each tribe.
:
Let p = time for the P tribe to shuck 300 oyster
then
(p+10) = time for T tribe to do it
:
= oysters/min of the P tribe
and
= oysters/min of the T tribe
:
Write an equation for the statement:
"the Pachena tribe shucks oysters at a rate of 5 oysters per minute faster than the Tchaika tribe,"
- 5 =
:
multiply by p(p+10), resulting in
300(p+10) - 5p(p+10) = 300p
300p + 3000 - 5p^2 - 50p = 300p
:
Combine like terms on the right
0 = 5p^2 +50p +300p - 300p - 3000
:
A quadratic equation
5p^2 + 50p - 3000 = 0
:
simplify, divide by 5
p^2 + 10p - 600 = 0
:
Factors to
(p+30)(p-20) = 0
:
the positive solution
p = 20 min to shuck 300 oysters
then
20 + 10 = 30 min to shuck 300 oysters per min for the T tribe
:
Find the rates
300/20 = 15 oysters/min
300/30 = 10 oysters/min, a difference of 5 per min

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