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To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the?
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To both start from point a and B of a river and traveled towards each ...
Let's call the distance between point A and point B x km.
When the two boats meet, the first boat has traveled x/2 km and the second boat has traveled x km.
If the first boat increases its speed to y km/h and both boats reach their respective destinations at the same time, it means that the time it took the first boat to travel from the point where they met to point B is the same as the time it took the second boat to travel from point A to point B.
If the time it takes for the first boat to travel from the point where they met to point B is t hours, then the distance traveled by the first boat is yt km. The distance traveled by the second boat is xt km.
We can set up the following equation:
y * t = x
5 * t = x/2
10 * t = x
Solving for t, we get:
t = x/10
Substituting this value of t back into the equation y * t = x, we get:
y = x/t = 10
The speed of the first boat, y, is 10 km/h. The stream speed is 5 km/h.
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To both start from point a and B of a river and traveled towards each ...
Problem Analysis:
Let's assume the distance between point A and point B is 'd' km. Both boats start from point A and point B and travel towards each other at the same speed of 5 km/h. Let's assume the time taken by both boats to meet each other is 't' hours.
Understanding the Problem:
The problem states that when the boats meet after the point, the first boat (which started from point A) increases its speed. The problem also mentions that both boats reach their respective destinations at the same time. We need to find the stream speed and the increased speed of the first boat.
Calculating the Distance Covered:
Since both boats are traveling towards each other, the total distance covered by both boats is equal to the distance between point A and point B. Hence, the distance covered by the first boat before they meet is 'd/2' km, and the distance covered by the second boat before they meet is also 'd/2' km.
Calculating the Time Taken:
Since the speed of both boats is 5 km/h, the time taken by both boats to meet each other is the same. We can use the formula distance = speed * time to calculate the time taken by both boats.
Time taken by the first boat = (d/2) / 5 = d/10 hours
Time taken by the second boat = (d/2) / 5 = d/10 hours
Calculating the Speed of the Stream:
Let's assume the speed of the stream is 's' km/h. The speed of the first boat after they meet will be 5 + s km/h. Since the time taken by both boats to reach their respective destinations is the same, we can use the formula distance = speed * time to calculate the distance covered by both boats after they meet.
Distance covered by the first boat after they meet = (5 + s) * (d/10) km
Distance covered by the second boat after they meet = 5 * (d/10) km
Since both boats reach their respective destinations at the same time, the distances covered by both boats after they meet should be equal.
(5 + s) * (d/10) = 5 * (d/10)
Simplifying the equation:
5 + s = 5
s = 0
Hence, the speed of the stream is 0 km/h.
Calculating the Increased Speed of the First Boat:
The problem states that the first boat increases its speed after they meet. Let's assume the increased speed of the first boat is 'v' km/h. The time taken by the first boat to reach its destination is d/(5 + v) hours.
Since the time taken by both boats to reach their destinations is the same:
d/10 = d/(5 + v)
Simplifying the equation:
10(5 + v) = 10
50 + 10v = 10
10v = -40
v = -4
Since the speed cannot be negative, the increased speed of the first boat is 4 km/h.
Summary:
- The speed of the stream is 0 km/h.
- The increased speed of the first boat is 4 km/h.
Explanation:
To summarize, when two
Let's assume the distance between point A and point B is 'd' km. Both boats start from point A and point B and travel towards each other at the same speed of 5 km/h. Let's assume the time taken by both boats to meet each other is 't' hours.
Understanding the Problem:
The problem states that when the boats meet after the point, the first boat (which started from point A) increases its speed. The problem also mentions that both boats reach their respective destinations at the same time. We need to find the stream speed and the increased speed of the first boat.
Calculating the Distance Covered:
Since both boats are traveling towards each other, the total distance covered by both boats is equal to the distance between point A and point B. Hence, the distance covered by the first boat before they meet is 'd/2' km, and the distance covered by the second boat before they meet is also 'd/2' km.
Calculating the Time Taken:
Since the speed of both boats is 5 km/h, the time taken by both boats to meet each other is the same. We can use the formula distance = speed * time to calculate the time taken by both boats.
Time taken by the first boat = (d/2) / 5 = d/10 hours
Time taken by the second boat = (d/2) / 5 = d/10 hours
Calculating the Speed of the Stream:
Let's assume the speed of the stream is 's' km/h. The speed of the first boat after they meet will be 5 + s km/h. Since the time taken by both boats to reach their respective destinations is the same, we can use the formula distance = speed * time to calculate the distance covered by both boats after they meet.
Distance covered by the first boat after they meet = (5 + s) * (d/10) km
Distance covered by the second boat after they meet = 5 * (d/10) km
Since both boats reach their respective destinations at the same time, the distances covered by both boats after they meet should be equal.
(5 + s) * (d/10) = 5 * (d/10)
Simplifying the equation:
5 + s = 5
s = 0
Hence, the speed of the stream is 0 km/h.
Calculating the Increased Speed of the First Boat:
The problem states that the first boat increases its speed after they meet. Let's assume the increased speed of the first boat is 'v' km/h. The time taken by the first boat to reach its destination is d/(5 + v) hours.
Since the time taken by both boats to reach their destinations is the same:
d/10 = d/(5 + v)
Simplifying the equation:
10(5 + v) = 10
50 + 10v = 10
10v = -40
v = -4
Since the speed cannot be negative, the increased speed of the first boat is 4 km/h.
Summary:
- The speed of the stream is 0 km/h.
- The increased speed of the first boat is 4 km/h.
Explanation:
To summarize, when two
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To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the?
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To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the?.
To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for To both start from point a and B of a river and traveled towards each other with the same speed of 5 km/h. The first vodka what’s half of the distance covered by the second boat when they meet after the point the first boat increases its speed and both the boards reach their respective destination at the same time. What was the stream speed an increasing the speed of the?.
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