Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current.

1- 7 mph

2- 3 mph

3- 2.5 mph

4- 4 mph

Question

Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current.
		
1-    7 mph
		
2-    3 mph
		
3-    2.5 mph
		
4-   4 mph

whpalmer4 · Answer

Have you done any problems like this before?

anonymous · Answer

no but i try them a lot but it does not work with me

whpalmer4 · Answer

Okay, no problem.  They are kind of fun once you know how to do them.

Julie and Eric row their boat (at a constant speed) 40 miles downstream for 4 hours, helped by the current. Rowing at the same rate, the trip back against the current takes 10 hours. Find the rate of the current.

Let's call the distance they row $x$.  We don't know how far it is, and it turns out not to matter.  

Do you know the formula to find the distance traveled if you know the speed and time?

anonymous · Answer

i know the destiny is 40 and the time is 4 and 10 but i try to do but i could not do them

anonymous · Answer

d=r*t

whpalmer4 · Answer

Good.  So let's call the speed of the boat in still water $v_s$, and the speed of the current $v_c$

When the boat goes with the current, the speed of the boat is $v_s+v_c$
When the boat goes against the current, the speed of the boat is $v_s - v_c$

Does that make sense?

anonymous · Answer

ok

whpalmer4 · Answer

Oh, I see we DO know the distance they travel.  40 miles.  

Rowing downstream (with the current), 

$$d = r * t$$$$40 \text{ miles} = (v_s + v_c)*(4\text{ hours})$$

Rowing upstream (against the current),
$$d = r*t$$$$40 \text{ miles} = (v_s - v_c)*(10\text{ hours})$$

For simplicity, I will drop the units and we will just remember that we are working in hours, and miles.

$$40 = 4(v_s+v_c)$$$$40 = 10(v_s-v_c)$$

That is a pair of equations in two unknowns.  Do you know how to solve it?

anonymous · Answer

not really

whpalmer4 · Answer

Well, let's start by using the distributive property to get rid of the parentheses.  What do you get if you expand those two equations?

anonymous · Answer

4u+4u
10u-10u

whpalmer4 · Answer

No. I will do one, you do the other.

$$40 = 4(v_s+v_c)$$$$40 = 4*v_s + 4*v_c$$$$40=4v_s + 4v_c$$ 

Now you do the other.  Use vs and vc for the two variable names.

$$40 = 10(v_s-v_c)$$

anonymous · Answer

40=10U-10U

anonymous · Answer

i do not know how to do ur U so

whpalmer4 · Answer

Those are two different variable names, maybe it is hard to see on your screen.  Let me start over and we will use $b$ for the speed of the boat in still water and $c$ for the speed of the current.

speed of boat going downstream: $b+c$
speed of boat going upstream: $b - c$

Is that clearer?

anonymous · Answer

yes

whpalmer4 · Answer

Then we have:
$$40\text{ miles} = (b+c) * 4\text{ hours}$$$$40 \text{ miles}= (b-c) * 10\text{ hours}$$
or dropping the units
$$40 = 4(b+c)$$$$40=10(b-c)$$

Now if we expand those two:
$$40 = 4b + 4c$$$$40 = 10b-10c$$

Okay?

anonymous · Answer

ok

whpalmer4 · Answer

That's a system of two equations in two unknowns.  We can solve it by substitution or elimination.  Do you know either of those methods?

anonymous · Answer

80=14b-6c

whpalmer4 · Answer

Substitution might be the easiest.  We take one equation, and solve it to give one variable in terms of the other.  

$$40 = 4b+4c$$$$40 - 4b = 4c$$$$10-b = c$$Now we take that expression for $c$ and replace $c$ wherever we find it in the other equation:
$$40 = 10b - 10c$$$$40 = 10b - 10(10-b)$$Can you solve that equation for $b$, please?

anonymous · Answer

ok
10*40=4b+4c
4*40=10b-10c

400=40b-40c
160=40b-40c

560=80b

b=7

c=3

anonymous · Answer

+40c
-40c

whpalmer4 · Answer

yes, b = 7 and c = 3 are correct.  The boat goes 7 mph in still water, so downstream it goes 10 mph, and upstream it goes 4 mph. 

Let's check that with the problem:

downstream we go 40 miles in 4 hours = 10 mph 
upstream we go 40 miles in 10 hours = 4 mph

both answer check out!

anonymous · Answer

only u can chose one  so i will see 7

anonymous · Answer

speed of the boot is 3 so 
3+4=7
3-10=7

anonymous · Answer

thanks buddy but i will write every word u have wrote in here thanks

anonymous · Answer

but the anwser was 3 gad

whpalmer4 · Answer

No the speed of the the boat is 7, the speed of the current is 3.

whpalmer4 · Answer

b=boat
c=current
we got b=7, c=3

anonymous · Answer

yes thanks

anonymous · Answer

i am just going to write how did u do the problem  so i can do it next time