SOLUTION: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the boat.

Question 1134473: A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the boat.
Found 4 solutions by josgarithmetic, Theo, MathTherapy, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
16, boat speed without current
c, speed of current

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A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the boat.
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The question asks for what was given.
The boat goes 16 mph in still water.
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let r = the speed of the boat in still water.
let w = the speed of the water.

the general equaation in still water is r * t = d.

when the boat is going downstream, the general equation becomes (r + w) * t = d

when the boat is going upstream, the general equation becomes (r - w) * t = d

you are given that the speed of the boat in still water is 16 miles per hour.

the downstream equation becomes (16 + w) * t = d
the upstream equaton becomes (16 - w) * t = d

you are given that the boat travels 15 miles downstream in the same time that it travels 9 miles upstream.

the downstream equation becomes (16 + w) * t = 15
the upstream equation becomes (16 - w) * t = 9

simplify both equations to get:

16 * t + w * t = 15
16 * t - w * t = 9

subtract the second equation from the first to get:

2 * w * t = 6

divide both sides of this equation by 2 to get:

w * t = 3

your original 2 equations of:

16 * t + w * t = 15
16 * t - w * t = 9

become:

16 * t + 3 = 15
16 * t - 3 = 9

subtract 3 from both sides of the first equation to get 16 * t = 12
add 3 to both sides of the second equation to get 16 * t = 12

solve for t in both equations to get t = 12/16 in each equation.

simplify to get t = 3/4 in each equation.

go back to your two original equations of:

(16 + w) * t = 15
(16 - w) * t = 9

replace t with 3/4 in these equations to get:

(16 + w) * 3/4 = 15
(16 - w) * 3/4 = 9

simplify these equations to get:

12 + 3/4 * w = 15
12 - 3/4 * w = 9

subtract the second equation from the first to get:

2 * 3/4 * w = 6

divide both sides of this equation by 2 to get:

3/4 * w = 3

solve for w to get w = 4.

that's your solution

the speed of the water is 4 miles per hour.

going downstream, the equation of (16 + w) * t = 15 becomes (16 + 4) * 3/4 = 15 which becomes 20 * 3/5 = 15 which becomes 15 = 15 which is true.

going upstream, the equation of (16 - w) * t = 9 bercomes (16 - 4) * 3/4 = 9 which becomes 12 * 3/4 = 9 which becomes 9 = 9 which is true.

the solution looks good.

the solution is that the speed of the water is 4 miles per hour.

in addition, we have solved for the time to be equal to 3/4 of an hour.

it is also posible to solve for w without first solving for t.

that could be done as follows:

your original equations to be solved are:

(16 + w) * t = 15
(16 - w) * t = 9

solve for t in both equations to get:

t = 15 / (16 + w) and t = 9 / (16 - w)

since t = t, then 15 / (16 + w) = 9 / (16 - w)

multiply both sides of this equation by (16 + w) * (16 - w) to get:

15 * (16 - w) = 9 * (16 + w)

simplify to get:

15 * 16 - 15 * w = 9 * 16 + 9 * w

add 15 * w to both sides of this equation and subtract 9 * 16 from both sides of this equation to get:

15 * 16 - 9 * 16 = 9 * w + 15 * w

simplify further to get 96 = 24 * w

solve for w to get w = 96 / 24 = 4

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A boat travels at 16 mph in still water. It takes the same amount of time for the boat to travel 15mi downstream as to go 9 mi upstream. Find the speed of the boat.

There are 2 boat speeds: one going downstream, and the other going upstream.
Let the speed of the current be C
Then we get the following TIME equation:
Solve the above for C, the current.
ADD the value of C to 16 to get the downstream speed and SUBTRACT the value of C from 16 to get the upstream speed.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

A normal solution to this problem should start from noticing that the posted question is   W R O N G.

The correct question must be   Find the speed of the current.

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