A boat on the potomac river travels the same distnace downstream in 2/3 hour as it does going upstream in 1 hr. If the speed of the curent is 3 mph, find the speed of the boat in the still water.

Question

phi · Answer

you need to know a few things:

1) rate * time = distance

2) the speed going with the current is faster than going against the current

if the current goes C and the boat goes B, going with the current, the speed is B+C

going against the current, the speed is B-C

phi · Answer

current is 3 mph,  so the speed with the current is B+3
the speed against the current is B-3

phi · Answer

downstream in 2/3 hour 

using rate * time = distance  we write
(B+3) * 2/3 = D  
we use the speed going with the current,  and time = 2/3 hour

phi · Answer

going upstream in 1 hr
write
(B-3) * 1 = D
using the speed going against the current, and time = 1  hour

phi · Answer

travels the same distance 
means we can say
(B+3) * 2/3 = (B-3) * 1

can you solve for B ?

anonymous · Answer

No, still have no idea what I'm doing

phi · Answer

There are a few parts to this problem.  One is finding the equations

The second part is doing the algebra.

phi · Answer

We can go over solving the equation  (without understanding how we got the equation)

start with 
(B+3) * 2/3 = (B-3) * 1

and solve for B.

first, notice on the right side you have (B-3)*1
you can simplify that to (B-3)   (because multiplying by 1 does not change (B-3) )

you have
$$ \frac{2}{3}(B+3) = B-3 $$
can you multiply both sides by 3?

anonymous · Answer

Yeah and it will take out the 3 in the 2/3 and then multiply it by -3 on the other side

so..   2b+6=b-9

phi · Answer

almost.

to multiply by both sides by 3,  write 3 times each side, like this
$$ 3\cdot \frac{2}{3}(B+3) = 3\cdot (B-3) $$
on the left side 3/3 is 1 so that simplifies to
$$ 2(B+3) = 3(B-3) $$
can you simplify both sides... by distributing the 2 on the left,  and 3 on the right side?

anonymous · Answer

2(B+3)=3(B-3)

2B+6=3b-9

then 2b-2b , and -2b from the 3b on the other side to get b

6=b-9

Then +9 and move it over to the 6 to get the b alone

15=B

phi · Answer

B stands for the Boat's speed.  so the answer to


find the speed of the boat in the still water. 

is 15 miles per hour