Question

Solve using Systems:

A boat traveled 440 miles downstream and back. The trip downstream took 11 hours. The trip
back took 22 hours. What is the speed of the boat in still water? What is the speed of the
current?
Speed of the boat in still water
Speed of the current

Answer 1

the answer is about 100

Answer 2

• boat: 30 mph
• current: 10 mph

Explanation:

Given that a 440 mi trip downriver took 11 hours, and the return trip took 22 hours, you want to know the speeds of the boat and current.

Sum

The trip downriver was at a speed of ...

speed = distance/time = 440 mi/(11 h) = 40 mi/h

Difference

The trip upriver was at a speed of ...

distance/time = 440 mi/(22 h) = 20 mi/h

Boat speed

The boat's speed is half the sum of these speeds:

(b + c) +(b -c) = 2b = (40 +20) mi/h

b = 30 mi/h

Current speed

The current's speed is the difference:

(b +c) = 40

c = 40 -b = 40 -30

c = 10 . . . mi/h

The speed of the boat in still water is 30 mi/h; the speed of the current is 10 mi/h.

__

Additional comment

We essentially wrote two equations:

• b + c = 40
• b - c = 20

using b = boat speed and c = current speed.

<95141404393>