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A motorboat travels 190 kilometers in 5 hours going upstream. It travels 330 kilometers going downstream in the same amount of time. What is the rate of the

boat in still water and what is the rate of the current?

1 Answer

6 votes

Answer:

  • boat: 52 km/h
  • current: 14 km/h

Explanation:

You want to know the speeds of boat and current given a 5-hour trip and an upstream distance of 190 km and a downstream distance of 330 km.

Upstream speed

Let b and c represent the speeds of boat and current, respectively. The speed upstream is ...

speed = distance/time

b -c = 190/5 = 38 . . . . . km/h

Downstream speed

Similarly, the downstream speed is ...

b +c = 330/5 = 66 . . . . . km/h

Boat speed

Adding the two equations gives ...

(b -c) +(b +c) = (38) +(66)

2b = 104

b = 52 . . . . . km/h

Current speed

Subtracting the first equation from the second gives ...

(b +c) -(b -c) = (66) -(38)

2c = 28

c = 14 . . . . . km/h

The speed of the boat in still water is 52 km/h; the speed of the current is 14 km/h.

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Additional comment

On planet Earth, you might have trouble finding a river 330 km long that has a current of 14 km/h over that length. Most rivers decline in speed to about 6 km/h after the initial plunge from the hills where they are born.

User Rory Byrne
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