Stations A and B are 60 km apart on a highway. One truck starts from A and the…
2025
Stations A and B are 60 km apart on a highway. One truck starts from A and the another one from B at the same time. If they travel in the same direction, they meet in 6 hours. But if they travel towards each other, they meet in one hour. The speeds of the two trucks are, respectively.
- A.
45 and 15 km/h
- B.
40 and 20 km/h
- C.
35 and 25 km/h
- D.
30 and 30 km/h
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Correct answer: C
Step-by-Step Solution
To determine the speeds of the two trucks, we can set up a system of linear equations based on their relative speeds in different scenarios.
Define the variables:
Let the speed of the first truck be x km/h and the speed of the second truck be y km/h (where x > y).
Analyze the two cases:
Same direction: When moving in the same direction, the relative speed is the difference between their speeds (x - y). They meet in 6 hours over a distance of 60 km.
(x - y) = Distance / Time = 60 km / 6 hours = 10 km/h
Opposite directions (towards each other): When moving towards each other, the relative speed is the sum of their speeds (x + y). They meet in 1 hour over a distance of 60 km.
(x + y) = Distance / Time = 60 km / 1 hour = 60 km/h
Solve the system of equations:
Equation 1: x - y = 10
Equation 2: x + y = 60
Add the two equations: 2x = 70, so x = 35 km/h.
Substitute x into Equation 2: 35 + y = 60, so y = 25 km/h.