The distance between town A and B is 30km. A cyclist riding at 8km/HR leaves town A and rides towards town B . At the same time, another cyclist riding at 12km/hr leaves town B for A . Calculate the distance from town A at which the two cyclist meet
Well, let's do some clowns calculations here! If the two cyclists are trying to meet each other, we can think of it like they are walking towards each other on a very long street.
The first cyclist is going at 8 km/hr and the second cyclist is going at 12 km/hr. So, they are coming at each other with a combined speed of 8 km/hr + 12 km/hr, which is 20 km/hr.
Since they are trying to meet each other, we can imagine that they are splitting the distance between town A and town B equally. So, they would meet each other at the halfway point.
The distance between town A and town B is 30 km, so the halfway point would be 30 km divided by 2, which is 15 km.
So, the two cyclists would meet each other 15 km from town A.
To calculate the distance from town A at which the two cyclists meet, we can use the concept of relative speed.
Relative speed is the combined speed of the two cyclists. In this case, the relative speed is 8 km/hr + 12 km/hr = 20 km/hr.
Since the two cyclists are riding towards each other, their combined distance covered per hour is equal to the relative speed.
Let's assume that the distance from town A where they meet is 'x' km.
Since the first cyclist is riding at 8 km/hr, the time taken by the first cyclist to reach the meeting point is x/8 hours.
Similarly, since the second cyclist is riding at 12 km/hr, the time taken by the second cyclist to reach the meeting point is x/12 hours.
Since they both start at the same time, the total time taken for them to meet is the sum of their individual times:
x/8 + x/12
Now, we can equate the time taken to meet with the distance to be covered:
x/8 + x/12 = 30
To solve this equation, we need to find the common denominator for 8 and 12, which is 24:
3x/24 + 2x/24 = 30
(3x + 2x)/24 = 30
5x/24 = 30
Cross-multiplying and solving for x:
5x = 30 * 24
5x = 720
x = 720/5
x = 144
Therefore, the distance from town A at which the two cyclists meet is 144 km.
To calculate the distance from town A at which the two cyclists meet, you can use the concept of relative speed.
First, let's determine the time it takes for the two cyclists to meet. Time can be calculated using the formula: Time = Distance / Speed.
Let "x" be the distance from town A where the cyclists meet.
Since both cyclists started at the same time, their travel times will be the same.
For the cyclist riding from town A, the distance traveled is "x" km, and the speed is 8 km/hr. So, the time taken by the cyclist from town A is: Time1 = x / 8.
For the cyclist riding from town B, the total distance traveled is 30 km - "x" km (as they meet at some point in between A and B), and the speed is 12 km/hr. So, the time taken by the cyclist from town B is: Time2 = (30 - x) / 12.
As they meet at the same time, Time1 = Time2:
x / 8 = (30 - x) / 12
Now, we can solve this equation to find the value of "x":
12x = 8(30 - x)
12x = 240 - 8x
20x = 240
x = 12
Therefore, the distance from town A at which the two cyclists meet is 12 km.
Time passed after the riders leave ---- t hrs
distance travelled by first rider = 8t
distance travelled by 2nd rider = 12t
8t + 12t = 30
20t = 30
t = 30/20 hrs = 3/2
distance covered by 1st = distance from town A = 8(3/2) = 12 km
check:
distance covered by the other = 12(3/2) = 18 km
and 12 km + 18 km = 30 km
my answer is correct