194k views
4 votes
A motorboat takes 5 hours to travel 150 miles going upstream. The return trip takes 3 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

User Pascual
by
7.6k points

1 Answer

3 votes

Answer:

rate of boat in still water = 40 mph

rate of current = 10 mph

Explanation:

speed of boat in still water = s

speed of current = c

speed upstream = s - c

speed downstream = s + c

time going upstream = 5 hours

time going downstream = 3 hours

distance = 150 miles

speed = distance/time

s = d/t

d = st

upstream:

d = st

150 = (s - c)(5)

s - c = 30 Eq. 1

downstream:

d = st

150 = (s + c)(3)

s + c = 50 Eq. 2

System of equations:

Equations 1 and 2 for a system of equations.

s - c = 30

s + c = 50

Add the equations and solve for s.

2s = 80

s = 40

Substitute 40 for s in Eq. 2 and solve for c.

s + c = 50

40 + c = 50

c = 10

Answer:

rate of boat in still water = 40 mph

rate of current = 10 mph

User Akenion
by
7.7k points