You drive your car 5.0 km due East at 35km/hr ...

Problem for the homework 3, chapter 3.

You drive your car 5.0 km due East at 35km/hr, and suddenly realize that you forgot your wallet.  So, you return home, driving West at 40 km/hr, and upon arrival spend 10 minutes looking for it, and finally go back on the road for a total of 57.0 km due East.  If your average speed was 40 km/hr for the whole journey, what was your average speed on your last leg?

a)46 km/hr

b)49 km/hr

c)35 km/hr

d) 40 km/hr

Solution

To East:

x₁=5km

V₁=35 km/h

t₁=x₁/v₁=(5km)/( 35 km/h)= 1/7 h

Back to home, driving West:

V₂=40 km/h

t₂=x₁/V₂=(5 km)/(40 km/h)=1/8 h

Looking time t₃=10 minutes = 1/6 h

Distance of the last leg due Est = 57 km

Distance Total (The total length of the total pass) = 5km+5km+57km=67km

V_{average total}=40km/h

Total time = (Distance Total)/ V_{average total} = (67km)/(40 km/h)

The time on the last leg = Total time – t₁-t₂-t₃ = (67km)/(40 km/h) – 1/7 h – 1/8 h – 1/6 h

The average speed on the last leg = (Distance of the last leg)/( The time on the last leg) = 57km/ ((67km)/(40 km/h) – 1/7 h – 1/8 h – 1/6 h)

Expression to the Google calculator:
57 km/ ((67 km)/(40 km/hour) – 1/7 hour – 1/8 hour – 1/6 hour) in km/hour

Google result: 45.950096 km / hour

Answer: a) 46 km/h