Question

Did I do this problem right? Warning: It's Very Long!!

Answer 1

Step 1:
Pick a friend or family member to be the character of your word problem. This friend or family member may do one of the following:
• Drive a boat
• Drive a jet ski
My father, Wayne, will be driving a boat.
Step 2:
Select a current speed of the water in mph.
The current speed will be 7 mph.
Step 3:
Select the number of hours (be reasonable please) that your friend or family member drove the boat or jets ski against the current speed you chose in step 2.
My father had to sail the boat upstream 60 miles in approximately 6 hours


Step 4:
Select the number of hours that your friend or family member made the same trip with the current (this should be a smaller number, as your friend or family member will be traveling with the current).
He will then have to sail the boat downstream for 72 miles in no less than 3 hours.
Step 5:
Write out the word problem you created and calculate how fast your friend or family member was traveling in still water. Round your answer to the nearest mph.

Wayne decided he wanted to take his daughter out for an all-day fishing trip. So, they packed up the truck and readied the fishing boat and high tailed it to the nearest doc. To get to his secret fishing spot, Wayne had to sail the boat upstream 60 miles in no less than 6 hours and then back downstream in no less than 3 hours, that is, if they want to make it home for dinner. Determine the speed Wayne must sail in still waters in order to make it home in time for dinner?

4. Follow the 5 steps below to complete this problem. (4 points)


My Solution:
c = current of river
b = rate of boat
d = s(t) will represent (distance = speed X time)

Upstream: 60 = 6(b-c)
Downstream: 72 = 3(b+c)

There are now two separate equations:
60 = 6b - 6c
and
72 = 3b + 3c

Solve both equations for b:
b = 10 + c
b = 24 - c
Now make both equations equal each other and solve for c:
10 + c = 24 - c
2c = 14
c = 7

The speed of the current was 7 mph
Now, plug the numbers into one of either the original equations to find the speed of the boat in still water.
I chose the first equation:
b = 10 + c
or
b = 10 + 7
b = 17
The speed of the boat in still water must remain a consistent 17 mph or more in order for Wayne and his daughter to make it home in time or dinner.

Answer 2

I know it looks extremely long but it's actually all part of the same question. If someone could just look over and tell me if I did it correctly, I would be truly grateful!!

Answer 3

my only quibble is that they want
Select the number of hours that your friend or family member made the *same trip* with the current
so you should go downstream only 60 miles rather than 72 miles. (Anyway, isn't that where you parked to car?)

Answer 4

ohh okay, I see now. Thanks, I missed that.. lol :D

Answer 5

but otherwise, it looks good.

Answer 6

Cool, thank you so much! :)

Answer 7

nearest doc. should be nearest dock.

Answer 8

haha thanks, btw wouldn't I have to change the whole solution if I change the one variable to 60 instead of 72?

Answer 9

definitely must change your solution, but it is not too hard (at least for me)...

Answer 10

haha funny... lets see how this works out. Im not very quick with this sort of stuff so It may take me a while. hahaha it took me forever to finish the first one, lol thanks again :)

Answer 11

Okay, here is my new solution:

My Solution:
c = current of river
b = rate of boat
d = s(t) will represent (distance = speed X time)

Upstream: 60 = 6(b-c)
Downstream: 60 = 3(b+c)

There are now two separate equations:
60 = 6b - 6c
and
60 = 3b + 3c

Solve both equations for b:
b = 10 + c
b = 10 - c
Now make both equations equal each other and solve for c:
10 + c = 10 - c
2c = 0
c = 0

The speed of the current was 0 mph
Now, plug the numbers into one of either the original equations to find the speed of the boat in still water.
I chose the first equation:
b = 10 + c
or
b = 10 + 0
b = 10
The speed of the boat in still water must remain a consistent 10 mph or more in order for Wayne and his daughter to make it home in time or dinner.

Is that better?

Answer 12

check this
60 = 3b + 3c

Answer 13

ohh your right! That would end up like this: 60 = 3(10) + 3(0) and that wouldn't work. What do I do?

Answer 14

redo 60= 3b+3c (solve for b, only doing it more carefully)

Answer 15

would 20 work?

Answer 16

yes. you can divide each term by 3 to get
20= b+c
b= 20 - c

somehow you got b = 10 - c , which isn't right.

Answer 17

I got confused I guess, haha

Answer 18

so pick up with
Solve both equations for b:
b = 10 + c
b = 20 - c

Answer 19

Now make both equations equal each other and solve for c:
10 + c = 20 - c
2c = 10
c = 5

The speed of the current was 5 mph
Now, plug the numbers into one of either the original equations to find the speed of the boat in still water.
I chose the first equation:
b = 10 + c
or
b = 10 + 5
b = 15
The speed of the boat in still water must remain a consistent 15 mph or more in order for Wayne and his daughter to make it home in time or dinner.

Better?

Answer 20

yes, perfect.

Answer 21

Awesome!! Thanks again!!

Answer 22

I have the same question but different numbers. I don't get how you did this could you help.
20 = 4 (b - c)
45 = 2 (b + c)

Answer 23

It is the same question as Renee99 at the top just with different numbers