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.
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.
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.
