"Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 20 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car?"

9.5 km/h

Explanation:

Let v₁ and v₂ be the rates of the cars.

Given that v₂ = v₁ - 20

The first car travels a distance v₁t in t = 5 hrs and the second car travels a distance of v₂t in t = 5 hrs. The total distance between them is 850 km.

So v₁t + v₂t = 850

  v₁t + (v₁ - 20)t = 850

v₁t + v₁t - 20t = 850

2v₁t - 20t = 850 at t = 5 hrs

2v₁ × 5 - 20 × 5 = 850

10v₁ - 100 = 850

10v₁ = 850 + 100

10v₁ = 950

v₁ = 950/10 = 9.5 km/h

v₂ = v₁ - 20 = 9.5 - 20 = -10.5 m/s

Since magnitude of v₁ < v₂

The rate of the slower car is 9.5 km/h

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