Two towns P and Q are 200 km apart. Bus X starts from Town P and Bus Y starts from Town Q at the same time. If the two buses travel towards each other, they meet after 2 hours. If they travel in the same direction, they cross each other after 8 hours. Find the speed of Bus X.
Well, let's look at the situation here. When the buses are traveling towards each other, we can consider their combined speed as the sum of their individual speeds. So, let's call the speed of Bus X as 'x' and the speed of Bus Y as 'y'.
Now, when they meet after 2 hours, their combined distance is 200 km, since they started from opposite ends. So, the equation we can set up is:
2(x + y) = 200
Solving this equation gives us:
x + y = 100
Now, when they travel in the same direction, we need to consider the relative speed of the two buses. Since they are moving in the same direction, the relative speed is the difference of their individual speeds. So we have:
8(x - y) = 200
Solving this equation gives us:
x - y = 25
Now, we have two equations with two variables:
x + y = 100
x - y = 25
Solving these equations will give us the speed of Bus X. But hey, instead of solving it seriously, let's solve it in a not-so-serious way, because I am Clown Bot after all!
Okay, let's add both these equations:
(x + y) + (x - y) = 100 + 25
Simplifying further:
2x = 125
So, x = 62.5
Therefore, the speed of Bus X is 62.5 km/h. But hey, don't take me too seriously, okay? I'm just a clown bot here to make you smile!
Let's assume the speed of Bus X as 'x' km/hr and the speed of Bus Y as 'y' km/hr.
When the two buses travel towards each other, their combined speed is the sum of their individual speeds:
Combined speed = x + y
Given that they meet after 2 hours, we can use the formula:
Distance = Speed × Time
Distance travelled by Bus X in 2 hours = x × 2
Distance travelled by Bus Y in 2 hours = y × 2
The total distance travelled by both buses when they meet is 200 km. So, we can set up the equation:
x × 2 + y × 2 = 200
Now, let's consider when the two buses travel in the same direction. In this case, their relative speed is the difference of their speeds:
Relative speed = x - y
Given that they cross each other after 8 hours, we can use the formula:
Distance = Speed × Time
Distance travelled by Bus X in 8 hours = x × 8
Distance travelled by Bus Y in 8 hours = y × 8
Again, the total distance travelled by both buses when they cross each other is 200 km. So, we can set up the equation:
x × 8 + y × 8 = 200
Now, we have a system of two equations:
2x + 2y = 200 ---(1)
8x + 8y = 200 ---(2)
We can simplify equation (1) by dividing both sides by 2:
x + y = 100
We can further simplify equation (2) by dividing both sides by 8:
x + y = 25
Since both simplified equations are equal to x + y, we can conclude that 100 = 25.
This means that the speed of Bus X is 100 km/hr.
Therefore, the speed of Bus X is 100 km/hr.
To find the speed of Bus X, we can use the formula:
Speed = Distance / Time
Let's calculate the speeds of both buses:
1. When the two buses travel towards each other:
- The total distance covered by both buses is 200 km (as they meet after 2 hours).
- Let's assume the speed of Bus X is v and the speed of Bus Y is u.
- The combined speed of both buses is v + u.
So, using the formula, we have:
(v + u) = 200 / 2
(v + u) = 100
2. When the two buses travel in the same direction:
- The relative speed between the two buses is the difference between their speeds.
- Let's assume Bus X is faster, so the relative speed is v - u, and they cross each other after 8 hours.
Using the formula again:
(v - u) = 200 / 8
(v - u) = 25
Now, we have a system of two equations:
(v + u) = 100
(v - u) = 25
We can solve this system by adding the two equations together:
(v + u) + (v - u) = 100 + 25
2v = 125
v = 125 / 2
v = 62.5
Therefore, the speed of Bus X is 62.5 km/h.
if the buses' speeds are x and y km/hr, since distance = speed * time
If X is the faster bus, then
2(x+y) = 200
8x = 8y+200
Now finish it off