Let's begin by understanding the information given in the problem:
1. Serena spent 2 hours traveling from city A to city B at a speed of 60 km/h.
2. She then spent 3 hours traveling from city B to city C.
3. The ratio of the speed from city A to city B to the speed from city B to city C is given as 3:4.
First, let's identify the speed from city A to city B:
- Speed from city A to city B is 60 km/h.
Next, we need to find the speed from city B to city C. We know that the ratio of the speed from city A to city B to the speed from city B to city C is 3:4. This means that if the speed from city A to city B is 3 units, the speed from city B to city C is 4 units.
Let's denote the speed from city B to city C as [tex]\( v_{B \to C} \)[/tex].
Since the ratio of the speed from A to B to the speed from B to C is 3:4, we can write:
[tex]\[ \frac{\text{Speed from A to B}}{\text{Speed from B to C}} = \frac{3}{4} \][/tex]
Given that the speed from A to B is 60 km/h, we can substitute this value into the ratio:
[tex]\[ \frac{60}{v_{B \to C}} = \frac{3}{4} \][/tex]
To find [tex]\( v_{B \to C} \)[/tex], we solve this equation:
[tex]\[ 60 = \frac{3}{4} \times v_{B \to C} \][/tex]
Multiplying both sides by 4 to eliminate the fraction:
[tex]\[ 60 \times 4 = 3 \times v_{B \to C} \][/tex]
[tex]\[ 240 = 3 \times v_{B \to C} \][/tex]
Now, divide both sides by 3 to isolate [tex]\( v_{B \to C} \)[/tex]:
[tex]\[ v_{B \to C} = \frac{240}{3} \][/tex]
[tex]\[ v_{B \to C} = 80 \][/tex]
Therefore, the speed from city B to city C is [tex]\( \boxed{80 \text{ km/h}} \)[/tex].
