Answer :
The speed of the first bus is 140 km/h, and the second bus's speed (13 km/h slower) is 140 - 13 = 127 km/h. Hence, the rate of each bus is 140 km/h and 127 km/h, respectively.
Let's assume that the speed of one bus is x km/h. Since the other bus is traveling 13 km/h slower, its speed will be (x - 13) km/h.
When two objects are moving towards each other, their combined distance covered is equal to the sum of their individual distances. In this case, the total distance covered by both buses is 1602 kilometers.
We can set up the equation as:
Distance = Speed * Time
For the first bus:
Distance covered by the first bus = Speed of the first bus * Time
Distance covered by the first bus = x km/h * 6 hours
For the second bus:
Distance covered by the second bus = Speed of the second bus * Time
Distance covered by the second bus = (x - 13) km/h * 6 hours
Since the total distance covered by both buses is 1602 kilometers, we can set up the equation:
x km/h * 6 hours + (x - 13) km/h * 6 hours = 1602 kilometers
Simplifying the equation:
6x + 6(x - 13) = 1602
6x + 6x - 78 = 1602
12x - 78 = 1602
12x = 1680
x = 140
Therefore, the speed of the first bus is 140 km/h, and the speed of the second bus (which is 13 km/h slower) is 140 - 13 = 127 km/h.
Hence, the rate of each bus is 140 km/h and 127 km/h, respectively.
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