Question 288541: A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
let speed of the boat in still water be x
let the speed of the current be y
upstream speed of boat is x-y
distance is 256
time is 4 hours
256 / x-y =4
Down stream
speed of boat = x+y
distance = 256
256/ x+y = 2
4x-4y=256------------1
2x+2y=256------------2
multiply eq 2 by 2
4x+4y=512-----------3
Add eq 1 & 3
4x-4y+4x+4y=512+512
8x=1024
x= 1024/8
=128 mph
plug the value of x in eq1
we get y=64mph speed of the current
Answer by ikleyn(53875)  (Show Source):
You can put this solution on YOUR website! .
A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The solution by @mananth in his post has arithmetic errors that lead to wrong answer.
In addition, the form of his presentation is MONSTROUS, which can not serve as a tool
for teaching or learning.
Therefore, I came with my alternative solution to replace the post by @mananth.
Let u be the rate of the motorboat in still water (in miles per hour)
and v be the rate of the current (in the same units).
Then the effective rate of the motorboat downstream is u + v miles per hour,
and the effective rate of the motorboat upstream is u - v miles per hour.
From the problem, the effective rate of the motorboat downstream is the distance of 256 miles
divided by the time of 2 hours  = 128 mph.
The effective rate of the motorboat upstream is the distance of 256 miles
divided by the time of 4 hours  = 64 mph.
So, we have two equations to find 'u' and 'v'
u + v = 128, (1)
u - v = 64. (2)
To solve, add equations (1) and (2). The terms 'v' and '-v' will cancel each other, and you will get
2u = 128 + 64 = 192 ---> u = 192/2 = 96.
Now from equation (1)
v = 128 - u = 128 - 96 = 32.
ANSWER. Under given conditions, the rate of the motorboat in still water is 96 mph.
The rate of the current is 32 mph km/h.
Solved.
-------------------------------
The reader should know that this problem and this type of problems @mananth "solves" using his computer code.
So, his posts are not a production of a human - they are production of a computer code,
and @mananth himself does not check his production (and even does not read it).
His computer code for this type of problem is written by an incorrect way, so every time
it produces the same type malformed version.
Therefore, at every appearance, I come and fix/repair his presentation to make sense from badly presented solution
and to keep this forum relatively clean from garbage.
@ikleyn
POST-SOLUTION note:
The given data in the problem are not realistic, and lead to unrealistic final answer.
Indeed, without explanations, it is obvious that the rate of the current of 32 miles per hour is too much
in order for some real motorboat would be able to move against the current, if it is not a fantastic story.
A normal and regular speed of the current in such problem is, usually, not more that 4 miles per hour.
This is a typical current speed for lowland rivers.
But this defect is not a defect of the solution - it is a product of the defective
and unsatisfactory job of the Math composer, i.e. the person, who created this Math problem.
Answer by n2(88)  (Show Source):
You can put this solution on YOUR website! .
A motorboat takes 4 hours to travel 256 mi going upstream. The return trip takes 2 hours going downstream.
What is the rate of the boat in still water and what is the rate of the current?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let u be the rate of the motorboat in still water (in miles per hour)
and v be the rate of the current (in the same units).
Then the effective rate of the motorboat downstream is u + v miles per hour,
and the effective rate of the motorboat upstream is u - v miles per hour.
From the problem, the effective rate of the motorboat downstream is the distance of 256 miles
divided by the time of 2 hours = 128 mph.
The effective rate of the motorboat upstream is the distance of 256 miles
divided by the time of 4 hours = 64 mph.
So, we have two equations to find 'u' and 'v'
u + v = 128, (1)
u - v = 64. (2)
To solve, add equations (1) and (2). The terms 'v' and '-v' will cancel each other, and you will get
2u = 128 + 64 = 192 ---> u = 192/2 = 96.
Now from equation (1)
v = 128 - u = 128 - 96 = 32.
ANSWER. Under given conditions, the rate of the motorboat in still water is 96 mph.
The rate of the current is 32 mph km/h.
Solved.
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