Raymond B. answered • 12/03/21
Math, microeconomics or criminal justice
exactly 25 mph in still water
25+4= 29 mph down stream
29 x 21 hours = 609 miles
upstream
25-4 = 21 mph
21 x 29 hours = 609 miles
Let b = speed of the boat in still water
b-4 = speed upstream
b+4 = speed downstream
Let t = time the boat travels upstream
50-t = time the boat travels upstream
d=rt, distance = rate of speed times time traveled
rt=d
(b-4)t = 609 miles
(b+4)(50-t) = 609 miles
two equations two unknowns
-bt +50b -4t + 200 = 609
bt -4t = 609
add to eliminate bt terms
-8t +50b +200 = 1218
subtract 200 from both sides
-8t +50b = 1018
b =(8t + 1018)/50 = (4t+509)/25
(b-4)t = 609
((4t + 509)/25 -4)t = 609
4t^2 + 409 t -15225 = 0
use the quadratic formula, or factor
(t-29)(t+525) = 0 (ignore negative solution)
t = exactly 29 hours upstream
b = (4t+509)/25
b = (4(29)+509)/25 = exactly 25 mph in still water
b-4 = 21. mph upstream
21 x 29 = 609
50-29 = 21 hours down stream
at 25+4 = 29 mph
29 x 21 = 609
or eliminate t and solve for b
(b-4)(25b-509) = 2436
25b^2 -609b - 400 = 0
use quadratic formula or factor
(b-25)(25b+16) = 0
b = 25 (ignore the negative solution)
Or another approach is try some t values
take (b-4)t = 609 and know that 50<t<25 for upstream time
so try a couple numbers for t, between 50 and 25, such as
some round numbers: 40 or 30
t=40, b = 609/40 + 4= 19.225. multiply both 40, to get 769
t=30 b = 609/30 + 4 = 20.3. multiply by 30 to get 609. looks very promising but
then downstream 20.3+4 = 24.3 times 20 = 486 which doesn't work
try t= 29
b= 609/29 - 4 = 21.
21 x 29 = 609 miles
(50-29)(25+4) = 609
try a few possibilities and narrow it down. boat speed in still water is exactly 25 mph
However you do it, when you get an exact integer solution, odds are you got the correct answer.
check the solution:
upstream (25-4)(29) =21(29) = 609
downstream (25+4)(21) = 29(21) = 609
