SOLUTION: the current in a stream moves at a speed of 9 mph. a boat travels 4 mi upstream and 4 mi downstream in a total of 4 hours. what is the speed of the boat in still water?

Question 808958: the current in a stream moves at a speed of 9 mph. a boat travels 4 mi upstream and 4 mi downstream in a total of 4 hours. what is the speed of the boat in still water?
Found 3 solutions by TimothyLamb, josgarithmetic, MathTherapy:
Answer by TimothyLamb(4379)   (Show Source): You can put this solution on YOUR website!
s = d / t
t = d / s
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4(miles)/(b + 9) + 4(miles)/(b - 9) = 4 hours
(1/4)(b + 9) + (1/4)(b - 9) = 1/4
(1/4)b + 9/4 + (1/4)b - 9/4 = 1/4
(1/2)b + = 1/4
b = 2/4
Answer:
Boat speed in still water is 0.5 mph
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Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
ASSIGN VARIABLES
r = boat speed when no current present
c = current speed
d = travel distance in either direction, up or down stream
h = time for round trip up and down stream for the d distance

QUESTION
Solve for r.

A data table may be very helpful.

DIRECTION___________Speed____________time(hour)___________Distance(miles)
Upstream____________r-c______________(___)________________d
Downstream__________r+c______________(___)________________d

Fill-in the time information.
DIRECTION___________Speed____________time(hour)___________Distance(miles)
Upstream____________r-c______________(d/(r-c))________________d
Downstream__________r+c______________(d/(r+c))________________d
Total_________________________________h

The data allows enough information to form a time sum equation.

Solution Steps:
which is multiply b.s. by LCD
, simplification and recognize difference of two squares

An important chief equation for our solution, entirely in symbolism.

You would want to solve that quadratic equation for r.
The values given in the description may be picked so that the highlighted quadratic equation may be factorable, but we never know ahead of time, unless we are specifically told so. In this solution, factorability is not assumed.

Directly using solution to quadratic formula,

------The answer purely in symbolic form.

Just substitute the given values from the description and compute r.

-----------------------------
So how about the quadratic equation found?
when the values are substituted.

While not being factorable, using this form for the general solution of a quadratic formula might be much easier than using purely symbolic form, but again, we never know this ahead of time. The advantage of doing all work in symbolic form is that if values are different but the basic form of the problem is the same, then you do not need to resolve the same problem again, because it would been already solved symbolically.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

the current in a stream moves at a speed of 9 mph. a boat travels 4 mi upstream and 4 mi downstream in a total of 4 hours. what is the speed of the boat in still water?

Let speed of boat in still water be S
Then average speed upstream = S � 9, and average speed downstream = S + 9

Therefore,

4(S + 9) + 4(S � 9) = 4(S - 9)(S + 9) ------ Multiplying by LCD, (S � 9)(S + 9)

Using the quadratic formula, the speed of the boat in still water = mph

You can do the check!!

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