Respuesta :
Given:
It takes the boat 3 hours to travel 108 miles going upstream
Return trip = 2hours going downstream
Distance, d = 108 miles
Time going upstream = 3 hours
Time going downstream = 2 hours
Let's find the rate in still water and the current rate.
Let s represent the still rate
Let c represent the current rate.
Apply the distance formula:
Distance = Rate x Time
We have the set of equations:
(s - c) x 3 = 108.................................Equation 1
(s + c) x 2 = 108.................................Equation 2
Apply distributive property:
3s - 3c = 108
2s + 2c = 108
Let's solve both equations simultaneously using substitution method.
Rewrite the first equation for s:
3s - 3c = 108
Add 3c to both sides:
3s - 3c + 3c = 108 + 3c
3s = 108 + 3c
Divide all terms by 3:
[tex]\begin{gathered} \frac{3s}{3}=\frac{108}{3}+\frac{3c}{3} \\ \\ s=36+c \end{gathered}[/tex]Substitute s for (36 + c) in equation 2:
2s + 2c = 108
2(36 + c) + 2c = 108
72 + 2c + 2c = 108
72 + 4c = 108
Subtract 72 from both sides:
72 - 72 + 4c = 108 - 72
4c = 36
Divide both sides by 4:
[tex]\begin{gathered} \frac{4c}{4}=\frac{36}{4} \\ \\ c=9 \end{gathered}[/tex]Substitute c for 9 in either of thee equation.
Take the first equation:
3s - 3c = 108
3s - 3(9) = 108
3s - 27 = 108
Add 27 to both sides:
3s - 27 + 27 = 108 + 27
3s = 135
Divide both sides by 3:
[tex]\begin{gathered} \frac{3s}{3}=\frac{135}{3} \\ \\ s=45 \end{gathered}[/tex]Thus, we have the solutions:
c = 9
s = 45
The rate of boat in still water is 45 miles per hour
The rate of the current is 9 miles per hour
Therefore, we have:
Rate of boat in still water: 45 mi/h
Rate of current: 9 mi/h
Take the firs
ANSWER:
Rate of boat in still water: 45 mi/h
Rae of the current: 9 mi/h
