Answer: 22 kph
Step-by-step explanation:
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) --> [tex]\dfrac{5}{2(x-2)}=t[/tex]
Downstream equation: 3 = t(x + 2) --> [tex]\dfrac{3}{x+2}=t[/tex]
Set the equations equal to each other to solve for x:
[tex]\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x[/tex]
Step-by-step explanation:
Step-by-step explanation:
distance (d) = rate (r) x time (t)
UPSTREAM: d = 5 km, r = *x - y, y = 2 kph, t = 2t
DOWNSTREAM: d = 3 k, r = *x + y, y = 2 kph, t = t
*x is the speed in still water and y is the current of the water.
Upstream equation: 5 = 2t(x - 2) --> \dfrac{5}{2(x-2)}=t
2(x−2)
5
=t
Downstream equation: 3 = t(x + 2) --> \dfrac{3}{x+2}=t
x+2
3
=t
Set the equations equal to each other to solve for x:
\begin{gathered}\dfrac{5}{2(x-2)}=\dfrac{3}{x+2}\\\\\\\text{Cross multiply:}\\5(x+2)=3\cdot2(x-2)\\\\\text{Distribute:}\\5x+10=6x-12\\\\\text{Isolate x:}\\10=x-12\\22=x\end{gathered}
2(x−2)
5
=
x+2
3
Cross multiply:
5(x+2)=3⋅2(x−2)
Distribute:
5x+10=6x−12
Isolate x:
10=x−12
22=x
