A boat is traveling in a river with a current that has a speed of 1.5 km/h. In one hour, the boat can travel twice the distance downstream as it can travel upstream. What is the boat's speed in still water?

Question

anonymous · Answer

Help!!!

anonymous · Answer

i hate word problems

anonymous · Answer

but i am sure we can do this using distance equals rate times time

anonymous · Answer

Me and my mom are having real hard problems with this. In class we are using the elimination method. I just can't figure it out

anonymous · Answer

We are also using d=rt

anonymous · Answer

we need a variable for the rate is still water
lets call it $x$ and see what equations we can come up with

anonymous · Answer

going downstream the rate will be $1.5$ faster so $x+1.5$ downstream
similarly upstream the rate will be $x-1.5$

anonymous · Answer

b+1.5=2(the upstream)
b-1.5=the uptream

anonymous · Answer

? Idk

anonymous · Answer

then  since $T=1$ we have 
$$x+1.5=2D\
x-1.5=D$$ and we can solve this one

anonymous · Answer

you can solve for $x$ using a number of methods. one way it to double the second one and get 
$$x+1.5=2D\
2x-3=2D$$ then solve 
$$2x-3=x+1.5$$

anonymous · Answer

Wouldn't it be
b=the speed of the boat in still water
c=the speed of the current
1.5=c
downstream=2(upstream)
So…
b+c=2(upstream)
b-c=upstream
Or...
b+1.5=2(upstream)
b-1.5=upstream

??

anonymous · Answer

calulate the speed im upstream 
then calculate in down strea (as its given twice divide by 2)
then take the difference in down and up stream

anonymous · Answer

i think instead of using the word "upstream" make that word "distance" or just D

anonymous · Answer

but they are equal 
so when you wrote 
$$b+1.5=2D\
b-1.5=D$$ that is really the same
double the second one get 
$$b+1.5=2D\
2b-3=2D$$ then set them equal to get 
$$b+1.5=2b-3$$

anonymous · Answer

Then substitute...
Upstream=b-1.5
2(upstream)=b+1.5
2(b-1.5)=b+1.5
2b-3=b+1.5?

anonymous · Answer

you had it right here 
b+1.5=2(upstream) 
b-1.5=upstream so again double the second one and set them equal

anonymous · Answer

yup looks good to me
solve that for $b$ in two steps and you are done

anonymous · Answer

@satellite73  but my method was correct,
 right?

anonymous · Answer

yes

anonymous · Answer

since one is twice as fast as the other we probably could have gone straight to 
$$2x-3=x+1.5$$

anonymous · Answer

Thank you!!!

anonymous · Answer

yw