SOLUTION: A motorboat travels the distance from one pier to another pier in 4 hours and the way back in 5 hours. What is the speed of the boat in still water if it travels 70 km with the cur

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Question 1207221: A motorboat travels the distance from one pier to another pier in 4 hours and the way back in 5 hours. What is the speed of the boat in still water if it travels 70 km with the current in 3.5 hours?
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
               SPEED          TIME       DISTANCE(kilometers)

GOING TO         r+c            4           d

RETURNING        r-c            5           d

condition        r+c            3.5          70

r, speed of boat without current
c, speed of the current

system%284%28r%2Bc%29=5%28r-c%29%2Cr%2Bc=70%2F3.5%29


See a very obvious substitution, for r+c.
system%284%2870%2F3.5%29=5r-5c%2Cr%2Bc=70%2F3.5%29

Simpler, system%285r-5c=80%2Cr%2Bc=20%29

Even still simpler
system%28r-c=16%2Cr%2Bc=20%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


I will leave it to other tutors to provide some form of a formal algebraic solution to the problem.

I will show a much faster and less formal solution that uses logical reasoning and simple mental arithmetic.

Obviously, the shorter 4-hour trip is with the current and the longer 5-hour trip is against the current.

The boat can travel 70km with the current in 3.5 hours.

Use that to determine that the speed of the boat with the current is 70/3.5 = 20km/h; then use that to determine that the distance of the trip is 4*20=80km.

Alternatively, you can do that calculation using a proportion that says the distance is proportional to the speed: x%2F70=4%2F3.5.

The trip is the same distance each direction. Since the ratio of times is 5:4, the ratio of speeds (with and against the current) is 4:5. So the speed against the current is 4/5 of the speed with the current: (4/5)(20) = 16km/h.

So the speed with the current is 20km/h and the speed against the current is 16km/h. Although it is a simple algebra problem to determine the speed of the current and the speed of the boat, logical reasoning tells us that the speed of the boat is halfway between 16km/h and 20km/h, or 18km/h, and the speed of the current is the difference between 18km/h and either 16km/h or 20km/h.

ANSWER: The speed of the boat in still water is 18km/h (and the speed of the current is 2km/h)

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
A motorboat travels the distance from one pier to another pier in 4 hours
and the way back in 5 hours. What is the speed of the boat in still water
if it travels 70 km with the current in 3.5 hours?
~~~~~~~~~~~~~~~~~~~~ 

70 km with the current in 3.5 hours means the speed downstream is  70/3.5 = 20 km/h.


The trip in 4 hours  downstream with the speed of 20 km/h means that one way distance is 20*4 = 80 km.


Spending 5 hours upstream the distance 80 km means that upstream speed is 80/5 = 16 km/h.


Having the speeds 20 km/h downstream and 16 km/h upstream means that the average of these two values is

    %2820%2B16%29%2F2 = 36%2F2 = 18 km/h.


This average is the speed of the boat in still water - so, the speed of the motorboat in still water is 18 km/h.    ANSWER

Solved.