help with a word problem..

Question

During the first part of a trip, a canoeist travels 16 miles at a certain speed. The canoeist travels 3 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip?

Answer 1

distance=rate*time

d=rt

first part of the trip...

16=rt

second part of the trip...

3=(r-5)(3-t)

16=rt implies r=(16/t)

substitute

3=[(16/t)-5][3-t]

3=(48/t)-15-16+5t

3=(48/t)-31+5t

multiply both sides by t

3t=48-31t+5t²

5t²-31t-3t+48=0

5t²-34t+48=0

factor this trinomial...

5*48=5*2*2*2*2*3, (5*2)(2*2*2*3), 10+24=34, the coefficient of the middle term

(5t-24)(t-2)=0

t-2=0

t=2 hours for the first part of the trip

16=rt

16=2r

16/2=r

8 mph=r, the rate for the first part of the trip

3=(8-5)(3-2)

3=3*1, 3 mph for the second part and 1 hour is the time

speeds are, again, 8 mph for the first 16 miles and 3 mph for the next 3 miles