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Jack rides in a motorboat against a river current for 36 km. Then he returns to his starting point by floating down river on a raft. Tommy travels 9 hours less on the motorboat than on the raft. Find the speed of the river current if the speed of the motorboat in still water is 15 km/h.

User Pierroz
by
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1 Answer

2 votes

Answer:

3 km/h

Explanation:

You want to know the speed of the river current if floating 36 km downstream takes 9 h longer than the trip upstream in a boat with a speed relative to the current of 15 km/h.

Time

The relation between time, speed, and distance is ...

time = distance / speed

If c represents the speed of the current, then 15-c is the speed upstream. The relation between the travel times is ...

36/(15 -c) = 36/c -9

Solution

Multiplying by c(15-c), we have ...

36c = 36(15 -c) -9(c)(15-c) . . . . . . . multiply by c(15-c)

36c = 540 -36c -135c +9c² . . . . . eliminate parentheses

9c² -207c +540 = 0 . . . . . . . collect terms

c² -23c +60 = 0 . . . . . . . . divide by 9

(c -20)(c -3) = 0 . . . . values that make the factors zero are c=20, c=3

The speed of the current is 3 km/h.

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Additional comment

The speed of the current cannot be greater than 15 km/h, or the boat could not go upstream. The speed of the current cannot be greater than 4 km/h, or the trip downstream would take less than 9 hours.

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User Friendly King
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