SOLUTION: In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 528 ​mi, in 6 hr.​ Returning, he finds th

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 528 ​mi, in 6 hr.​ Returning, he finds th      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1049079: In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 528

​mi, in 6

hr.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 5.5

hr. Find the rate of​ Bill's boat and the speed of the current. Let x​ = the rate of the boat in still water and y​ = the rate of the current.
Found 2 solutions by josgarithmetic, advanced_Learner:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Constant Travel Rate Rule to relate rate, time, distance corresponding to R, T, D, is RT=D. 
                SPEED           TIME         DISTANCE
UPSTREAM        x-y             6            528
DOWNSTR         x+y             5.5          528


You have a system of equations, system%28%28x-y%29%2A6=528%2C%28x%2By%29%2A%285.5%29=528%29.
Solve the system. Both equations are linear.

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
the required equations are
528%2F6=u-v for upstream
528%2F5.5=u%2Bv for downstream

88=u-v
96=u%2Bv

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cu+%2B+-1%5Cv+=+88%2C%0D%0A++++1%5Cu+%2B+1%5Cv+=+96+%29%0D%0A++We'll use substitution. After moving -1*v to the right, we get:
1%2Au+=+88+-+-1%2Av, or u+=+88%2F1+-+-1%2Av%2F1. Substitute that
into another equation:
1%2A%2888%2F1+-+-1%2Av%2F1%29+%2B+1%5Cv+=+96 and simplify: So, we know that v=4. Since u+=+88%2F1+-+-1%2Av%2F1, u=92.

Answer: system%28+u=92%2C+v=4+%29.