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A riverboat travels 78 km downstream in 3 hours. It travels 80 km upstream in 4 hours. Find the speed of the boat and the speed of the stream.

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User Arcadian
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1 Answer

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Answer: Let's call the speed of the boat "b" and the speed of the current "c". We can set up two equations based on the information given:

Downstream: distance = rate × time

78 = (b + c) × 3

Upstream: distance = rate × time

80 = (b - c) × 4

Now we have two equations with two unknowns, which we can solve simultaneously. We can start by simplifying each equation:

78 = 3b + 3c

80 = 4b - 4c

We can solve the second equation for "b" by adding 4c to both sides and then dividing by 4:

80 + 4c = 4b

20 + c = b

Now we can substitute this expression for "b" into the first equation and simplify:

78 = 3(20 + c) + 3c

78 = 60 + 6c

18 = 6c

c = 3

So the speed of the current is 3 km/h. We can use the expression we found for "b" earlier to find the speed of the boat:

b = 20 + c = 20 + 3 = 23 km/h

Therefore, the speed of the boat is 23 km/h.

Explanation:

User Tajinder
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