alegbra question?

Question

I have no idea how to do this one...i found a similar one where the distance was 15mph and the top speed was the same and the ans was 3 and 1/3

anyways heres the question
A motorboat goes 18 miles downstream at its top speed and then turns around and returns 18 miles upstream at top speed. The trip upstream took twice as long as the trip downstream. If the boat's top speed is 10 mph in still water, how fast is the current? (Hint: If the current speed is r miles per hour, then the motorboat travels at (10 + r) mph downstream and at (10 - r) mph upstream.)

Express your answer as a decimal rounded to the nearest hundredth.

Answer 1

since it takes twice as long, the upstream would be
2(10-r)
so set the two equal
2(10-r)=10+r
20 - 2r = 10 + r
10 = 3r
3.33=r

Answer 2

speed of the motoboat traveling downstream is 10 + r
speed of the motoboat traveling upstream is 10 - r


time = distance / speed

the time it takes the motoboat to travel upstream is twice the time it takes the motoboat to travel downstream

time for upstream:
t1 = 18/(10-r)

time for downstream:
t2 = 18/(10+r)

t1 = 2 * t2

so 18/(10-r) = 2(18)/(10+r)

18/(10-r) = 36/(10+r)

36(10-r) = 18(10+r)

360 - 36r = 180 + 18r
180 = 54r
r = 3 1/3 mile/hr

Answer 3

How could the distance be 15 mph in your example?

OK let 'r' be the rate of the current, you have to find.
Let 't' be the time to go downstream.
Distance over Speed equals Time.
Downstream: 18/(10 + r) = t
Upstream: 18/(10 - r) = 2t
We have simultaneous equations in 2 unknowns.
Multiply #1 by (10 + r) to remove fractions:
18 = t(10 + r)
Multiply #2 by (10 - r) to remove fractions:
18 = 2t(10 - r)
Eliminate the common distance:
10t + rt = 20t - 2rt
Collect like terms:
3rt = 10t
Divide by t:
3r = 10 or r = 3.33 mph

Answer 4

Wow - this is a hard question.

Let t= time downstream

then (10+r)t=18 - speed in mph x time in hours = 18 miles

Time upstream was twice as long, or 2t, so:

(10-r)2t=18

Since 18 = 18 I can substitute:

(10+r)t = (10-r)2t

Distribute:
10t+rt = 20t - 2rt
rt = 10t - 2rt subtract 10t from both sides

3rt = 10t add 2rt to both sides

3r = 10 divide both sides by t

r = 10/3 or 3 1/3 divide both sides by 3.

Answer is current r is 3 1/3 mph.

Answer 5

You can do it like this:

You will first need to express both UP and DOWN trip in terms of time, because the problem says "twice as long". This is the condtion where both will equal to each other. Although it says "long", it is really talking about time.

distance / speed = time

DOWN stream time is as follows:
18/(10+r)

On the other hand, UP stream time is as follows
18/(10-r)

Now, you know, UP stream took twice as long as down, so you have:

UP = DOWN * 2

Now combine both equation and you get this:

18/(10-r) = 2(18/(10+r))

Now, solving this...

18/(10-r) = 36/(10+r) remove the 2 before parenthesis...
36(10-r) = 18(10-r) cross multiply
360 - 36r = 180 + 18r
-36r - 18r = 180 - 360
-54r = - 180
r = 180/54

r = 3.33

Then, the speed of the current is 3.33mph

Answer 6

multiply brackets flow the y's to the main appropriate, and the x's to left 3y-6x+18 = 27 8x-6x = 4-2y flow x & # to top Do math 3y = 27 + 6x - 18 2x = 4 - 2y 3y = 9 + 6x multiply with the help of -one million divide the two aspects with the help of -2x = -4 + 2y 3 flow -4 to left ingredient y = 3 + 2x 4 - 2x = 2y Divide with the help of two 2 - x = y replace the cost of y 2 - x = 3 + 2x crew 2-3 = 2x + x -one million = 3x divide with the help of three -one million/3 = x Substitue the cost of x for one among the different equations 2 - x = y 2 - (-one million/3) = y 2+ one million/3 = y 6/3 + one million/3 = y y = 7/3