Answer:
The current flows at 5 mph.
Step-by-step explanation:
Let the rate at which the current flows be c, and that of the boat in still water be b.
Recall that distance = rate times time. Thus,
(c + b)(3 hrs) = 120 mi, or c + b = 40 mi/hr
((b - c)(4 hrs) = 120 mi, or b - c = 30 mi/hr
We need to solve this system of linear equations for c.
c + b = 40
b - c = 30
combining these equations yields
2b = 70, and so b = 35 mph
Subbing 35 mph into the 2nd equation, above, yields 35 mph - 30 mph = 5 mph (answer)
Answer:
Current = 5 mph
Step-by-step explanation:
Let the rate of the boat = r
Let the rate of the current = c
Trip There
d = 120
t = 3
r = r + c
Equation
120/(r + c) = 3
Trip Back
d = 120
t = 4
r = r - c
Equation
120/(r - c) = 4
Solution
Equation 1: 120 = 3 (r + c)
Equation 2: 120 = 4 ( r - c)
Equation 1: divide both sides by 3: 40 = r + c ...... Equation 3
Equation 2: divide both sides by 4: 30 = r - c ....... Equation 4
Add (3) + (4)
40 = r + c
30 = r - c
70 = 2r Divide by 2
r = 70/2
r = 35
Use equation 3 to solve for c
40 = 35 + c Subtract 35 from both sides.
40 - 35 = c
c = 5
