Question

During the first part of a trip, a canoeist travels 59 miles at a certain speed. The canoeist travels 17 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?

Answer 1

round to the nearest hundredth

Answer 2

okay, we will do this one together

Answer 3

okay

Answer 4

now we have to use the formula, d=r*t

Answer 5

for the first part of the trip: a canoeist travels 59 miles at a certain speed, which means that we can now write our equation d=r*t as 59=(r*t) sub 1. The reason i right sub1 is becuase we will have to equation like this one and i want to be able to distinguish between both okay

Answer 6

okay

Answer 7

now, The canoeist travels 17 miles on the second part of the trip at a speed 5 mph slower. This means that our equation d=r*t, can be written as 17=((r-5)*t)sub 2, okay.

Answer 8

okay

Answer 9

the reason i wrote r-5 is because the canoest is traveling 5 miles slower

Answer 10

to recap, we have:

59=(r*t) sub 1
and

17=((r-5)*t)sub 2

Answer 11

okay

Answer 12

Now, the total time for the trip is 5hrs, which means that our last equation can be written as:

t sub1+t sub 2=3 okay

Answer 13

t represnets the time , so logically, the two t variables in our equations when added together give the total time of 3 hrs

Answer 14

okay

Answer 15

now we have 3 equations:

59=(r*t) sub 1


17=((r-5)*t)sub 2


and

t sub1+t sub 2=3 okay

Answer 16

okay

Answer 17

lets begin with the first equation, we have 59=(r*t) sub 1, now we can rearrgane this okay, that way we can solve for tsub1, now in this case tsub1=59/r

17=((r-5)*t)sub 2, same this with the second equation: tsub2=17/r-5

Answer 18

now with these to values, we look a the third equations: t sub1+t sub 2=3.

We now know what tsub 1 and tsub2 represent. We simply plug in those values.

and we get

(17/r-5)+ (59/r)=3

Answer 19

okay

Answer 20

Still stuck

Answer 21

made a mistake on it should be: (17/r-5)+ (59/r)=5

Answer 22

ohhh okay so now I am way confused

Answer 23

now we will take that new equation, and multiply it through by the common denominator of r(r-5). It will look like this:



(r(r-5))((17/r-5)+ (59/r)=3), which after evluation will be: 59(r-5)+17(r)=5(r(r-5))

Answer 24

what numbers would I plug in for r?

Answer 25

now all we do is distribute: 59r-295+17r=5r^2-25r

Answer 26

okay

Answer 27

now we simply collect like terms, and we get: 5r^2-101r+295

Answer 28

Okay

Answer 29

that is one of the last steps.

Answer 30

then either use the quadratic formula to solve this, or a calculator. I get x as being:

x=3.5417 or x=16.568

since we cannot subtract 5 from 3.5417 (we would get a negative value) the we take 16.568 as being our answer. Which means that the speed on the first part of the trip was about 16.568mph