During the first of a trip, a canoeist travels 35 miles at a certain speed. The canoeist travels 7 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?

Question

During the first of a trip, a canoeist travels 35 miles at a certain speed. The canoeist  travels 7 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?

anonymous · Answer

?= mph

anonymous · Answer

You can set the speed of the first part as x and the second as x-5. You know that the trip took a total of 2 hours. Because speed if just miles/hour and you know the miles traveled at the certain speed, you can use the following equation to solve for the speed:
$$2hr=35mi/x(mi/hr)+7mi/(x-5)(mi/hr)=35/x*(hr)+7/(x-5)*(hr)$$
Now that everything is in hours, just solve for x...

anonymous · Answer

Rounding to the nearest hundredth

llort · Answer

(35/t(a)-s(a))-(7/t(b)+5-s(b))=2

Am I on the right track?

anonymous · Answer

the first was 22.03

llort · Answer

I mean:

(35/t(a)-s(a))+(7/t(b)+5-s(b))=2

dumbcow · Answer

use d = r*t
t1 + t2 = 2 --> t1 = 2-t2
35 = r*t1 --> 35 = r(2-t2) --> t2 = 2 - (35/r)
7 = (r-5)t2
7 = (r-5)(2-35/r)
7 = 2r + 175/r - 45 
multiply everything by r and set equal to 0
2r^2 - 52r + 175 = 0
r = 52 + sqrt(52^2 - 1400) / 4
r = 22.028

anonymous · Answer

and the second one

dumbcow · Answer

what does the question say....5 mph slower

anonymous · Answer

The second speed is just 5 less than the first: 17.03