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.
Answers
Step-by-step explanation:
Let x be the speed of current
Use formula, D=RT
Upstream: D1=(15-x)(T+4)=15T+60-xT-4x Eq 1
Downstream: D2=(15+x)(T)=15T+xT. Eq 2
But D1=D2, so 15T+60-xT-4x=15T+xT
2xT+4x=60
xT+2x=30 by division of 2 to reduce to lowest term
x(T+2)=30
x=30/(T+2) but D1=D2=63
Substitutions:
D2=15T+xT=63; 15T+xT=63; 15T+30/(T+2)=63 due to the substitution of x=30/(T+2)
15T+30T/T+2=63
[15T(T+2)+30T]/(T+2)=63
15T^2+30T+30T=63T+126
15T^2–3T=126
T^2–0.20T=8.40 by dividing by 15
T^2–0.20T-8.40=0 Quadratic Equation
Using Formula for Quadratic Equation: T={0.20+-[(0.2)^2–4(1)(-8.40)]^1/2}/2(1)
T=(0.20+-5.80)/2 use + sign to avoid negative answer for Time
T=(0.20+5.80)/2=6/2=3 hours for downstream
For Upstream, T=3+4= 7 hours
Solve for current using Eq2: D2=15T+ xT but D2=63
63=15(3)+x(3)= 45+3x
63=45+3x
3x=63–45=18
x=18/3= 6 km/hr speed of current
Check:
Downstream Time=3 hours
Upstream Time= 7 hours
So the difference of 3 and 7 is 4 hours
D= RT upstream, T=D/R=63/15–6=63/9= 7 hours ok
D=Rt downstream, T=63/15+6=63/21= 3 hours ok