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A motorboat travels 190 kilometers in 5 hours going upstream. It travels 260 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?

2 Answers

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To solve this problem, you need to realize that the speed of the boat going downstream (with the current) will be faster than the speed of the boat going upstream (against the current).

Let's denote:

- The rate of the boat in still water as "b" (in km/h), and

- The rate of the current as "c" (in km/h).

When the boat is moving upstream (against the current), the effective speed of the boat is (b - c) because the current is slowing it down. We know that it travels 190 km in 5 hours, so we can write this as an equation:

190 = 5 * (b - c) [Equation 1]

When the boat is moving downstream (with the current), the effective speed of the boat is (b + c) because the current is speeding it up. It travels 260 km in 5 hours, so we can write this as a second equation:

260 = 5 * (b + c) [Equation 2]

This is a system of two equations with two variables that we can solve. First, let's simplify each equation:

From equation 1:

b - c = 190/5 = 38 [Equation 1 simplified]

From equation 2:

b + c = 260/5 = 52 [Equation 2 simplified]

Now, we can solve this system of equations. If we add these two simplified equations together, we find that:

2b = 38 + 52 = 90

b = 90/2 = 45 km/h

Substitute b = 45 km/h into the simplified equation 1:

45 - c = 38

c = 45 - 38 = 7 km/h

Therefore, the speed of the boat in still water is 45 km/h and the speed of the current is 7 km/h.

User Daouda
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2 votes

Answer:

speed of boat in still water = 45 km/h

speed of water = 7 km/h

Explanation:

Let s = speed of boat in still water.

Let w = speed of water.

speed = distance/time

distance = speed × time

When the boat goes downstream, the speed of the water adds to the speed of the boat. When the boat goes upstream, the speed of the water decreases the speed of the boat.

speed downstream: s + w

speed upstream = s - w

Upstream:

distance = 190 km

time = 5 hours

distance = speed × time

190 = (s - w) × 5

5s - 5w = 190

Downstream:

distance = 260 km

time = 5 h

distance = speed × time

260 = (s + w) × 5

5s + 5w = 260

We have a system of equations.

5s - 5w = 190

5s + 5w = 260

Add the equations.

10s = 450

s = 45

5s - 5w = 190

5(45) - 5w = 190

-5w = -35

w = 7

Answer:

speed of boat in still water = 45 km/h

speed of water = 7 km/h

User Scott Bellware
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7.9k points