A and B are two points 150 km apart on a highway.two cars start from A and B at the same time if they move in the same direction they meet in 15 hours but if they move in the opposite direction they meet in 1 hour find their speeds
If the speeds are a and b, then under suitable assumptions, since distance = speed*time,
15a+150 = 15b
a+b = 150
now just solve for a and b.
A=70
B=80
To find the speeds of the two cars, let's assume the speed of the first car is "x" km/h and the speed of the second car is "y" km/h.
When the cars are moving in the same direction, their relative speed is the difference between their individual speeds:
Relative speed when moving in the same direction = x - y
Since they meet in 15 hours when moving in the same direction, and they are 150 km apart, we can use the formula: Distance = Speed × Time
150 = (x - y) × 15
Now, let's consider when the cars are moving in opposite directions. In this case, their relative speed is the sum of their individual speeds:
Relative speed when moving in opposite directions = x + y
They meet in 1 hour when moving in the opposite direction, so we can use the formula: Distance = Speed × Time
150 = (x + y) × 1
Now, we have a system of two equations:
1) 150 = (x - y) × 15
2) 150 = (x + y) × 1
Simplifying equation 2, we get:
150 = x + y
From equation 2, we can rewrite y in terms of x:
y = 150 - x
Substituting this value of y into equation 1, we can solve for x:
150 = (x - (150 - x)) × 15
150 = (2x - 150) × 15
150 = 30x - 2250
30x = 2400
x = 80
Now that we have the value of x, we can substitute it back into equation 2 to find the value of y:
150 = 80 + y
y = 70
Therefore, the speed of the first car is 80 km/h, and the speed of the second car is 70 km/h.