Question

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 60.0 min at 85.0 km/h, 12.0 min at 85.0 km/h, and 50.0 min at 60.0 km/h and spends 15.0 min eating lunch and buying gas.

(a) Determine the average speed for the trip. km/h

(b) Determine the distance between the initial and final cities along the route. km

Answer 1

Speed of the person in the first part = V₁ = 85 km/hr

Time period of the first part = T₁ = 60 min = 1 hour

Distance traveled by the person in the first part = D₁

D₁ = V₁T₁

D₁ = (85)(1)

D₁ = 85 km

Speed of the person in the second part = V₂ = 85 km/hr

Time period of the second part = T₂ = 12 min = 0.2 hours

Distance traveled by the person in the second part = D₂

D₂ = V₂T₂

D₂ = (85)(0.2)

D₂ = 17 km

Speed of the person in the third part = V₃ = 60 km/hr

Time period of the third part = T₃ = 50 min = 0.833 hours

Distance traveled by the person in the third part = D₃

D₃ = V₃T₃

D₃ = (60)(0.833)

D₃ = 50 km

Total distance traveled by the person = D

D = D₁ + D₂ + D₃

D = 85 + 17 + 50

D = 152 km

Total time taken = T

T = T₁ + T₂ + T₃

T = 1 + 0.2 + 0.833

T = 2.033 hours

Average speed for the trip = V_avg

V_avg = 74.76 km/hr

a) Average speed for the trip = 74.76 km/hr

b) Distance between the initial and final cities along the route = 152 km