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Traveling downstream a certain boat went 16 mph. Traveling upstream it only went 4 mph. What is the speed of the current? How fast would the boat go if there were no current?

User Fragorl
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1 Answer

4 votes

The speed of current is 6 mph. If there is no current, then boat would go with speed of 10 mph

Solution:

Formula to remember for this problem:

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then:

Speed downstream = (u + v) km/hr

Speed upstream = (u - v) km/hr

Given that Traveling downstream a certain boat went 16 mph

let s = the boat speed in still water

let c = the rate of the current

s + c = 16 --- eqn 1

Also given that Traveling upstream it only went 4 mph

s - c = 4 ----- eqn 2

Add eqn 1 and eqn 2

s + c = 16

s - c = 4

(+) ----------------

2s = 20

s = 10

Substitute s = 10 in eqn 1

10 + c = 16

c = 6

Thus the speed of current is 6 mph

How fast would the boat go if there were no current?

We have found out that speed of current is 6 mph

If there is no current means,

s - c = 4

s - 6 = 4

s = 10 mph

Thus if there is no current, then boat would go with speed of 10 mph

User Eboni
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8.1k points
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