Question

A boat makes 120-mile trip downstream in 3 hours but makes the return trip ok 4 hours . What is the rate of the current

Answer 1

The current flows at 5 mph.

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 2

Current = 5 mph

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