SOLUTION: Ineed your help once again I try own my own and my answer are looking craazt help is needed. Thank you so much Steve traveled 200 miles at a certain speed. Had he gone 10mph fa

Question 172638This question is from textbook
: Ineed your help once again I try own my own and my answer are looking craazt help is needed. Thank you so much
Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle
can you show me this one too.
The Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?
This question is from textbook

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
I set up the equations you solve
:
d=rt........in both instances distance is equal
lets call the rate of the slow trip r and time t
lets call the rate of the fast trip r+10 and time(t-1)
:
so 200=rt...eq 1
...200=(r+10)(t-1)..eq 2
:change eq 1 to t=200/r and substitute it into eq 2 and solve for r...this will involves a quadratic equation again
:

throw out negative value
so mph and =50mph
:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=8100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 40, -50. Here's your graph:

:
:
:
:
Let s= speed of the boat in still water
The current =3 mi/hr
we know that d=rt or d/r=t for this problem we must break this up into 2 parts
(distance upriver)/(rate going upriver)
+ (distance downriver)/(rate going downriver) = 9 hrs
:the we know the distance is 60 each way
the rate going up stream is 60/s-3
the rate going down stream is 60/s+3
:
so we have again a quadratic equation
:
:
multiply each term by (s+3)(s-3)
:

:
drop the negative value
:
so mph

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=17316 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13.9772373998204, -0.643904066487102. Here's your graph:

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