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 spee

Question 1149799: 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 of the river.

Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

The time equation is - = 4 hours. It is literal translation English to Math. 63*(15+x) - 63*(15-x) = 4*(15^2-x^2) Reduce this quadratic equation to the standard form and solve it by any method you know. Here x is the speed of the current. // Without any complicated calculations, I see the answer by my non-armed eye: x= 6 miles per hour for the rate of the current. You may confirm it by solving quadratic equation formally.

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To see many other similar solved problems, see the lessons
    - Wind and Current problems
    - More problems on upstream and downstream round trips
    - Wind and Current problems solvable by quadratic equations
    - Unpowered raft floating downstream along a river
    - Selected problems from the archive on the boat floating Upstream and Downstream
in this site, where you will find other similar solved problems with detailed explanations.

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The referred lessons are the part of this textbook under the section "Word problems", the topic "Travel and Distance problems".

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Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
d=v*t
63=(15+c)*t where c is current speed
t=63/(15+c)
and
63=(15-c)(t+4)
and t=[63/(15-c)]-4, which is (4c+3)/(15-c), from putting -4 over 15-c and getting -60+4c
those t s are equal
cross-multiply and get 2c^2+63c-450=0
and this is (2c+75)(c-6)=0
positive root is c=6 kph current
this would be 21 kph downstream and 3 hours to do 63 km and 9 kph upstream, which takes 7 hours.
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