Question

a person travels by car from one city to another with different constant speeds between pairs of cities.she drives for 30 min at 80 km/h,12 min at 100km/h,and 45 min at 40 km/h and spends 15 min eating lunch and buying gas.a)determine the average speed for the trip.b)determine the distance between the initial and final cities along the route

Answer 1

Question#24540

a person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 30 min at 80 km/h, 12 min at 100 km/h, and 45 min at 40 km/h and spends 15 min eating lunch and buying gas. Determine the average speed for the trip. Determine the distance between the initial and final cities along the route

Solution:

Let:

$$\begin{array}{l} t_{1} = 30 \text{ min} = 0.5 \text{ h} \\ t_{2} = 12 \text{ min} = 0.2 \text{ h} \\ t_{3} = 45 \text{ min} = 0.75 \text{ h} \\ t_{4} = 15 \text{ min} = 0.25 \text{ h} \\ v_{1} = 80 \text{ km/h} \\ v_{2} = 100 \text{ km/h} \\ v_{3} = 40 \text{ km/h} \\ \end{array}$$ $$\begin{array}{l} v = ?, \quad S = ? \\ S = S_{1} + S_{2} + S_{3} = v_{1} * t_{1} + v_{2} * t_{2} + v_{3} * t_{3} \\ S = 80 * 0.5 + 100 * 0.2 + 40 * 0.75 = 90 \text{ km} \\ v = \frac{S}{t_{1} + t_{2} + t_{3} + t_{4}} = \frac{90}{0.5 + 0.2 + 0.75 + 0.25} = 53 \text{ km/h} \\ \end{array}$$

Answer: the average speed is 53 km/h, the distance between cities is 90 km.