SOLUTION: the speed of a boat in still water is 15 km/hr. it needs four more hours to travel 63 km against the current of a river than it needs to travel down the river. Determine the speed

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the speed of a boat in still water is 15 km/hr. it needs four more hours to travel 63 km against the current of a river than it needs to travel down the river. Determine the speed       Log On


   

Question 1131057: the speed of a boat in still water is 15 km/hr. it needs four more hours to travel 63 km against the current of a river than it needs to travel down the river. Determine the speed
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
the speed of a boat in still water is 15 km/hr.
it needs four more hours to travel 63 km against the current of a river than it needs to travel down the river.
Determine the speed of the current
:
Let c = the rate of the current
then
(15-c) = actual speed against the current
and
(15+c) = actual speed with the current
:
Write a time equation: time = dist/speed
Upstream time - downstream time = 4 hrs
63%2F%28%2815-c%29%29 - 63%2F%28%2815%2Bc%29%29 = 4
multiply equation by (15-c)(15+c), cancel the denominators
63(15+c) - 63(15-c) = 4(15-c)(15+c)
945 + 63c - 945 + 63c = 4(225-c^2)
126c = 900 - 4c^2
form a quadratic equation on the left
4c^2 + 126c - 900 = 0
Use the quadratic formula a=4; b=126; =-900
I got solutions of
c = -37.5, not reasonable
and
c = 6 km/hr is the speed of the current
:
:
See if that works, find the actual time each way, (9 km/hr up & 21 km/hr down)
63/9 = 7 hrs
63/21= 3 hrs
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time dif: 4 hrs