Question

A tugboat goes upstream 160 miles in 10 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current and the speed of the current.

Answer 1

Thank you

Answer 2

Let me know what you get for b and c

Answer 3

I got 16 for b and 32 for c

Answer 4

How is it possible that b < c when we need b - c to be positive?

Answer 5

I am not sure. honestly I have been stuck on this question for almost an hour.

Answer 6

Hint: use d = rt, where r = (b ± c)

160 = 10(b-c)
160 = 5(b+c)

Solve the system

Answer 7

Try that and see what you get

Answer 8

I got c=16 and b=32. so the tugboat goes 32 mph and the speed of the current would be 16. Thank you for your help.

Answer 9

No, sorry, that still is not correct. I have no clue how you are going about solving this

Answer 10

I show you that

160 = 10(b-c)
160 = 5(b+c)

The next step would be to divide both sides of the first equation by 10, and both sides of the second equation by 5 to get:

16 = b - c
32 = b + c

However, we need to find b and c separately.

Answer 11

I am solving it by eliminating the c or b. Like I stated above, I have been at this equation for an hour just about, I am confused on how to solve for this. I am sorry for miss understanding you, I just do not get it.

Answer 12

I'm pretty sure you got

16 = b - c
32 = b + c

in your initial steps. The problem is, we are not done yet.

Answer 13

We're not done until we isolate one of the variables and find a specific value for it

Answer 14

If you think about it, we have a system of equations here. And we can easily eliminate c by adding both equations together. If we do that we get

48 = 2b

Answer 15

so if 48=2b, we would divide both sides by 2?

Answer 16

Yes, but the important thing is that you understand how I got to 48 = 2b

Answer 17

you took 16=b-c
32=b+c and you added both sides together, so that is how you got 48=2b. 16+32=48 and b+b 1+1= 2 I have noticed you could not do this to c, because a negative plus a positive would eliminate the c all together.

Answer 18

Okay, so have you actually solved for b yet?

Answer 19

If so, what did you get?

Answer 20

b=24

Answer 21

Okay, so if b = 24, what is c?

Answer 22

c would equal 0 if we used this term by adding the equations together.

Answer 23

That was only to eliminate c so that we could solve for b. That doesn't mean c equals zero.

Answer 24

c could equal any number. The way you get zero is by taking whatever number you have and subtracting that same number to get zero.

10 - 10 = 0
16 - 16 = 0
4 - 4 =0
a - a = 0
b - b = 0

those are just examples, but they show that those are numbers that are subtracted to get zero. But of course 10 ≠ 0, 16 ≠ 0, 4 ≠ 0, a ≠ 0, b ≠ 0, and in this case c ≠ 0

Answer 25

would c=8 if we plugged 24 in an equation?

Answer 26

Actually, it is 8. My bad. Good job

Answer 27

Finally...you had me confused at certain points too

Answer 28

Thank you, you had me re think myself, because both sides gave me 8

Answer 29

so 24 would be the mph and 8 would be the current?

Answer 30

24 mph = speed of the boat
8 mph = speed of the current

That's why I used b and c as variables of course

Answer 31

thank you for you help, I am glad we used it this way. you made it less confusing. :)

Answer 32

As a general rule the speed of the boat must be greater than the speed of the current. Otherwise, the boat would not get to its destination.

Answer 33

Okay. I will remember that.

Answer 34

Also another thing you need to remember is this:

Upstream = boat against current = b - c
downstream = both with current = b + c

This is why the equations are setup as such

Upstream:
160 = 10(b-c)

Downstream:
160 = 5(b+c)