Question

During the first part of a trip, a canoeist travels 30 miles at a certain speed. The canoeist travels 12 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 2 hrs. What was the speed on each part of the trip?
Please round to the nearest hundredth.
I am really stuck and am in need of the answers. I have worked this problem many times and keep getting the first part wrong.

Answer 1

well everytime I did the math you gave me it came up wrong

Answer 2

Sorry

Answer 3

I get the second part but not the first part. If I can get the answer to the first part I will be okay.

Answer 4

It is the first part I am getting wrong.

Answer 5

work back words...

Answer 6

I have worked this problem so many time my head hurts. I can never get the first part of the problem right.

Answer 7

well if you know the speed of 2nd part, just add 5 to get speed of 1st part
he was going 5mph slower on 2nd part

Answer 8

yeah that is what is confusing to me

Answer 9

ok say he went 10mph for 1st trip
then he went 5mph for 2nd trip
or in general
speed r in 1st trip, (r-5) in 2nd trip

Answer 10

my head hurts

Answer 11

haha im sorry
ok what answer did you get, we can check to see if its right

Answer 12

28.46 for the first and 23.46 for the second but it tells me it is wrong

Answer 13

distance = rate*time
1st part:
30 = 28.46 * t1
t1 = 1.05
2nd part:
12 = 23.46*t2
t2 = 0.51
we know
t1+t2 = 2
however
1.05+0.51 = 1.56
thats why its wrong

Answer 14

man dumbcow you are amazing!!!

Answer 15

okay so I am off by not much

Answer 16

haha, i've been doing this for awhile

Answer 17

yeah not me. I stink at math.

Answer 18

ok so go back and replace those numbers with r and (r-5)
that will represent the speeds
try to solve for r again

Answer 19

the equations should be
t1 = 30/r
t2 = 12/(r-5)
t1 +t2 = 2

Answer 20

okay I feel stupid r stands for?

Answer 21

sorry

Answer 22

speed of 1st trip

Answer 23

use whatever variable you want really

Answer 24

okay this is the only problem I have been stuck on I will just take the hit my brain hurts and I am getting tired

Answer 25

haha ok
i'll show you the solution, just try to work it out on your own later

Answer 26

okay thank you.

Answer 27

Substitute in equations for t1 and t2
\[\frac{30}{r} + \frac{12}{r-5} = 2\]
combine fractions, get common denominator
\[\frac{30}{r}*\frac{r-5}{r-5} + \frac{r}{r}*\frac{12}{r-5} = 2\]
\[\frac{30(r-5) + 12r}{r(r-5)} = 2\]
Bring denominator to other side
\[30(r-5) +12r =2r(r-5)\]
\[30r -150 +12r = 2r^{2} -10r\]
Set equal to zero
\[2r^{2}-52r+150 = 0\]
Factor out a 2
\[r^{2} -26r +75=0 \]
Use quadratic formula, a =1, b=-26, c =75
\[r = 3.3, 22.695\]
r must be greater than 5
\[r = 22.695\]

Answer 28

Again thank you. I will copy this and work it over and over till I understand it.