Question

A boat traveled 240 miles downstream and back. The trip downstream took 10 hours. The trip back took 30 hours. What is the speed of the boat in Stillwater? What is the speed of the current?

Answer 1

A boat traveled 120 miles downstream and back.
The trip downstream took 6 hours.
The trip back took 15 hours.
Find the speed of the boat in still water and the speed of the current.
:
Let s = speed in still water
Let c = speed of the current
then
(s+c) = effective speed downstream
and
(s-c + effective speed upstream
:
Write a distance equation for each trip; dist = time * effective speed
6(s+c) = 120

15(s-c) = 120
Simplify both these equations, divide the 1st by 6; divide the 2nd by 15, results:
s + c = 20
s - c = 8
--------------adding these equations eliminate c, find s
2s = 28
s = 14 mph speed in still water
then
s + c = 20
14 + c = 20
c = 20 - 14
c = 6 mph is the current

Answer 2

Speed of the boat in Still water = 16 mph

Speed of the current = 8 mph

Explanation:

Let the speed of stream be s and speed of boat in still water be b.

Relative velocity during downstream motion = b + s

Relative velocity during upstream motion = b - s

Time taken for downstream motion = 10 hours

Time taken for upstream motion = 30 hours

Distance traveled by boat = 240 miles

Downstream motion:

Distance traveled by boat = Relative velocity during downstream motion x Time taken for downstream motion

240 = ( b + s) x 10

b + s = 24 -------------------- eqn 1

Upstream motion:

Distance traveled by boat = Relative velocity during upstream motion x Time taken for upstream motion

240 = ( b - s) x 30

b - s = 8 -------------------- eqn 2

eqn 1 + eqn 2

b + s + b - s = 24 + 8

2b = 32

b = 16 miles per hour

Substituting in eqn 1

16 + s = 24

s = 8 miles per hour

Speed of the boat in Still water = 16 mph

Speed of the current = 8 mph