Question

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

3 mph
4 mph
5 mph

Answer 1

With the current 40 miles per hour
Against the current 30 miles per hour
bv means boat velocity with NO current
cv means current velocity
A) bv + cv = 40 mph
B) bv - cv = 30 mph
Adding both equations:
2bv = 70
boat velocity with NO CURRENT = 35 miles per hour

Using equationA
bv + cv = 40
35 + cv = 40

current velocity = 5 miles per hour

Answer 2

Speed of current = 5 mph

Explanation:

Let u be the speed of boat and v be the speed of current.

A boat makes a 120-mile trip downstream in 3 hours.

120 = 3(u+v)

u + v = 40

It makes the return trip in 4 hours.

120 = 4(u-v)

u - v= 30

Adding both equations

u + v + u - v = 40+30

2u = 70

u = 35 mph

35 + v = 40

v = 5 mph

Speed of current = 5 mph