Question

A house boat sailed 30 miles Downstream in 3 hours and return to the same Marina Upstream in 5 hours. Find the rate of the house boat in still water and the rate of the current in the water.

Answer 1

• houseboat speed: 8 mph
• current speed: 2 mph

Explanation:

The downstream speed is ...

speed = distance/time = 30 mi/(3 h) = 10 mi/h

The upstream speed is ...

distance/time = 30 mi/(5 h) = 6 mi/h

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The downstream speed is the sum of boat speed (b) and current speed (c):

b + c = 10

The upstream speed is their difference:

b - c = 6

Adding these two equations gives ...

2b = 16

b = 8 . . . . . boat speed is 8 mph

Then the current speed is ...

c = 10 -b = 10 -8 = 2 . . . . . current speed is 2 mph