A boat is crossing a wide river flowing at 8 km/hr. from west to east. The landing port is exactly the opposite of the starting point on the south bank of the river. If the boat moves at 10 km/hr. to cross the river and crosses it in 1/2 hr., what is the width of the river?
Question
A boat is crossing a wide river flowing at 8 km/hr. from west to east. The landing port is exactly the opposite of the starting point on the south bank of the river. If the boat moves at 10 km/hr. to cross the river and crosses it in 1/2 hr., what is the width of the river?
Solution
To find the width of the river, we can use the concept of relative velocity.
Let's assume the width of the river is 'x' km.
The boat is moving at a speed of 10 km/hr. relative to the water. Since it takes 1/2 hr. to cross the river, the distance it travels in that time is 10 km/hr. * 1/2 hr. = 5 km.
Now, let's consider the velocity of the river. The river is flowing at a speed of 8 km/hr. from west to east. Since the boat is crossing from west to east, it will be affected by the velocity of the river.
To find the effective velocity of the boat, we need to subtract the velocity of the river from the velocity of the boat. So, the effective velocity of the boat is 10 km/hr. - 8 km/hr. = 2 km/hr.
Since the boat travels 5 km in 1/2 hr. with an effective velocity of 2 km/hr., we can set up the equation:
Distance = Speed * Time 5 km = 2 km/hr. * 1/2 hr.
Simplifying the equation, we get: 5 km = 1 km
Therefore, the width of the river is 5 km.
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