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Answer :
Answer:
78 km/h
Step-by-step explanation:
Let s represent the speed of the slower car. The total speed of the two cars is their closing speed:
(s) + (s+14 km/h) = (340 km)/(2 h)
2s + 14 km/h = 170 km/h . . . . . simplify
s + 7 km/h = 85 km/h . . . . . . . . divide by 2
s = 78 km/h . . . . . . . . . . . . . . . . subtract 7 km/h
The rate of the slower car is 78 km/h.
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Final answer:
The rate of the slower car is 78 kilometers per hour. This is determined by setting up an equation based on their combined distance covered and solving for the slower car's speed.
Explanation:
To solve this problem, let's denote the rate of the slower car as x kilometers per hour (km/h). Since one car's rate is 14 km/h more than the other's, the faster car moves at x + 14 km/h. Both cars are heading towards each other, meaning their speeds will be added when calculating the closing speed.
They cover a total distance of 340 kilometers and meet after 2 hours. The equation modeling their total distance covered (D) during this time (T) is: D = (x + (x + 14)) × T. Substituting the given values gives 340 = 2(x + x + 14), which simplifies to 340 = 4x + 28.
To find the rate of the slower car, solve for x: 340 - 28 = 4x, which simplifies to 312 = 4x, therefore x = 78 km/h. Hence, the rate of the slower car is 78 km/h.
