Question

Can someone help me work through this problem please , Having trouble understanding . Its Systems of equations.

Answer 1

what is the problem?

Answer 2

4. Follow the 5 steps below to complete this problem. (4 points)
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
Step 2:
Select a current speed of the water in 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.
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).
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.

Answer 3

its a 5 step equation

Answer 4

good lord, okay i guess we can try this

Answer 5

haha, you can see my struggle !

Answer 6

how about i learn how to read. you are not supposed to pick the speed of the boat, you are supposed to pick the current
how about 4 mph for the current?

Answer 7

Sounds good .

Answer 8

so 4 mph for the current

Answer 9

so lets start with
1) justin drives a boat upstream and back
2) the current is 4 mph
3) it takes him 5 hours to go up steam
4) it takes him 4 hours to come back

Answer 10

so far so good?

Answer 11

Very!

Answer 12

so now we have to solve it

Answer 13

Thats where i have the trouble at

Answer 14

damn
okay we can do that too. i suppose the question is
a) how far did he go or?
b) what is the speed of the boat in still water?

Answer 15

so lets call the rate in still water \(r\) for "rate" and the distance he travelled \(D\) for distance. since the current is 4 mph the rate with the current is \(r+4\) and the rate against the current is \(r-4\)
so far so good?

Answer 16

now we can use "distance equals rate times time"
the rate with the current is \(r+4\) and the time with the current is 4 hours
the rate against the current is \(r-4\) and the time against the current is 5 hours
since the distance going is evidently the same as the distance returning, you know that
\[D=(r-4)\times 5=(r+4)\times 4\]

Answer 17

in other words, your last job is to solve
\[5(r-4)=4(r+4)\] for \(r\)
that is the last step

Answer 18

so you just distribute
5(r-4)= 4(r+4)
5r-20 =4r+16?

Answer 19

yup

Answer 20

add the common factors
5r-20 =4r+16?
5r 5r
20= r+16 ?
16 16
4 =r

Answer 21

last steps not so good
lets start with
\[5r-20=4r+16\] and subtract \(4r\) from both sides

Answer 22

ok
so
5r−20=4r+16
4r 4r
r -20=16?

Answer 23

yes, better
now add 20 to both sides

Answer 24

r-20=16
20 20
r= 36

Answer 25

yes, good
on your first attempt you actually made two mistakes \(4r-5r=-r\) not \(r\) and also you dropped the minus sign in front of the 20

Answer 26

so if you had wanted to solve by subtracting \(5r\) from both sides it would have looked like
\[4r-20=4r+16\]
\[-20=-r+16\]
\[-36=-r\]
\[36=r\]

Answer 27

I get my negatives and postives mixed up im pretty bad with that. /: thanks for the help !
i appreciate it !

Answer 28

yw, good luck!!

Answer 29

could you help me with one more?