Question

A man on a road trip drives a car at different constant speeds over several legs of the trip. He drives for 50.0 min at 55.0 km/h, 15.0 min at 65.0 km/h, and 45.0 min at 45.0 km/h and spends 20.0 min eating lunch and buying gas.

(a)

What is the total distance traveled over the entire trip (in km)?

(b)

What is the average speed for the entire trip (in km/h)?

Answer 1

Time period of the first part = T₁ = 50 min = 50/60 hours = 0.8333 hours

Speed of the car in the first part = V₁ = 55 km/hr

Distance traveled in the first part = D₁

D₁ = V₁T₁

D₁ = (55)(0.8333)

D₁ = 45.83 km

Time period of the second part = T₂ = 15 min = 15/60 hours = 0.25 hours

Speed of the car in the second part = V₂ = 65 km/hr

Distance traveled in the second part = D₂

D₂ = V₂T₂

D₂ = (65)(0.25)

D₂ = 16.25 km

Time period of the third part = T₃ = 45 min = 45/60 hours = 0.75 hours

Speed of the car in the third part = V₃ = 45 km/hr

Distance traveled in the third part = D₃

D₃ = V₃T₃

D₃ = (45)(0.75)

D₃ = 33.75 km

Time period the man stops for eating lunch and buying gas = T₄ = 20 min = 20/60 min = 0.3333 hours

Total distance traveled over the trip = D

D = D₁ + D₂ + D₃

D = 45.83 + 16.25 + 33.75

D = 95.83 km

Total time period of the trip = T

T = T₁ + T₂ + T₃ + T₄

T = 0.8333 + 0.25 + 0.75 + 0.3333

T = 2.1666 hours

Average speed for the entire trip = V_avg

V_avg = 44.23 km/hr

a) Total distance traveled over the entire trip = 95.83 km

b) Average speed for the entire trip = 44.23 km/hr