SOLUTION: A thee hour river cruise goes 15km upstream and then back again. The river has a current of 2km an hour. What is the boat's speed and how long was the upstream journey?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A thee hour river cruise goes 15km upstream and then back again. The river has a current of 2km an hour. What is the boat's speed and how long was the upstream journey?      Log On


   

Question 807766: A thee hour river cruise goes 15km upstream and then back again. The river has a current of 2km an hour. What is the boat's speed and how long was the upstream journey?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
r = boat speed if no current present.
c = 2 km/h current of river.
u = time going upstream
3-u = time going downstream (based on description and on assignment of u)


________________speed____________time___________distance(km)
Upstream________r-c______________(u)__________(___)
Downstream______r+c______________(3-u)__________(___)
Total______________________________3_____________15


Two unknown variables , r and u. Filling in the distance data,
________________speed____________time___________distance(km)
Upstream________r-c______________(u)__________((r-c)(u))
Downstream______r+c______________(3-u)__________((r+c)(3-u))
Total______________________________3_____________15


The "Total" data gives an equation:
%28r-c%29%28u%29%2B%28r%2Bc%29%283-u%29=15
'
Steps
ru-rc%2B3r%2B3c-ur-uc=15
ru-rc%2B3r-r%2B3c-uc=15
r%28u-c%2B3-1%29%2B3c-uc=15
r%28u-c%2B2%29=15%2Buc-3c
r=%2815%2Buc-3c%29%2F%28u-c%2B2%29
Substituting for c=2,
r=%2815%2B2u-6%29%2F%28u%29
highlight%28r=%289%2B2u%29%2Fu%29 This is still one equation in TWO unknown variables.

This will have infinite solutions but there is a restriction.
highlight%280%3Cu%3C3%29 is that restriction. You may compute r accordingly for its RANGE.