Two bicycles start from two different points on a straight road. The first bicycle travels at a constant speed of 18 km/h towards the east while the second bicycle travels at a constant speed of 12 km/h. Towards the west if the two bicycles start at the same time from a point that is 36km/h away from each other, how long does it take to cross each other at what distance from each starting point?
Let's assume the distance from the starting point to where the bicycles cross each other is x km from the first bicycle's starting point.
The first bicycle is traveling at a speed of 18 km/h towards the east, so its distance covered in time t is 18t km.
The second bicycle is traveling at a speed of 12 km/h towards the west, so its distance covered in time t is 12t km.
Since the two bicycles started at the same time, their total distance covered is the sum of their distances covered individually. This is given by:
18t + 12t = 36
30t = 36
t = 36/30
t = 6/5 hours
To find the distance from each starting point, we can substitute the value of t in either of the two equations. Let's use the equation for the distance covered by the first bicycle:
Distance covered by the first bicycle = 18*t
Distance covered by the first bicycle = 18 * (6/5)
Distance covered by the first bicycle = (18 * 6)/5
Distance covered by the first bicycle = 108/5 km
Therefore, it would take 6/5 hours (or 1.2 hours), for the bicycles to cross each other. The distance from the first bicycle's starting point to where they cross is approximately 21.6 km.
To find out how long it takes for the two bicycles to cross each other, we need to determine the time it takes for them to cover the distance between them.
Let's denote the distance between the two starting points as d = 36 km.
Since the bicycles are moving in opposite directions, their relative speed is the sum of their individual speeds:
Relative Speed = Speed of Bicycle 1 + Speed of Bicycle 2
Relative Speed = 18 km/h + 12 km/h
Relative Speed = 30 km/h
To find the time it takes for them to cross each other, we can use the formula:
Time = Distance / Relative Speed
Time = 36 km / 30 km/h
Time = 1.2 hours
Therefore, it takes 1.2 hours (or 1 hour and 12 minutes) for the bicycles to cross each other.
To find the distance from each starting point, we can use the formula:
Distance = Speed x Time
For Bicycle 1:
Distance = 18 km/h x 1.2 hours
Distance = 21.6 km
For Bicycle 2:
Distance = 12 km/h x 1.2 hours
Distance = 14.4 km
Therefore, the distance from the starting point for Bicycle 1 is 21.6 km and for Bicycle 2 is 14.4 km.
To solve this problem, we need to find the time it takes for the two bicycles to meet and the distance from each starting point where they meet.
Let's assume that the distance traveled by the first bicycle before they meet is "x" kilometers. Since the first bicycle is traveling towards the east, its distance from the starting point will be 36 - x km.
The time taken by the first bicycle to cover this distance can be calculated using the formula:
Time = Distance / Speed
For the first bicycle: Time1 = (36 - x) / 18 = (36 - x) / 18
Similarly, the distance traveled by the second bicycle before they meet is also "x" kilometers. As the second bicycle is traveling towards the west, its distance from the starting point will be 36 - x km.
The time taken by the second bicycle can be calculated using the same formula:
Time2 = (36 - x) / 12 = (36 - x) / 12
Since both bicycles start at the same time, the total time taken by the two bicycles to meet is the sum of the individual times:
Time1 + Time2 = (36 - x) / 18 + (36 - x) / 12
To find when the two bicycles meet, we have to set up an equation:
(36 - x) / 18 + (36 - x) / 12 = t
Where "t" represents the total time taken to meet.
Simplifying the equation:
[2(36 - x) + 3(36 - x)] / 36 = t
(72 - 2x + 108 - 3x) / 36 = t
(180 - 5x) / 36 = t
180 - 5x = 36t
To find the distance from the starting point where the two bicycles meet, we can use either bicycle's equation:
Distance = Speed x Time
For the first bicycle: Distance1 = 18t = 36t km
For the second bicycle: Distance2 = 12t = 36t km
So, the two bicycles meet at a distance of 36t km from each starting point.
To find the values of "t" and "36t", we need to solve the equation.
Since "t" and "36t" represent time and distance, respectively, it's not possible to find a specific answer to this problem without knowing the total time "t". This additional information is required to calculate the time and distance accurately.