A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 35.0 min at 100.0 km/h, 10.0 min at 55.0 km/h, and 45.0 min at 35.0 km/h and spends 35.0 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

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Question:

A person travels by car from one city to another with different constant speeds between pairs of cities. She drives for 35.0 min at 100.0 km/h, 10.0 min at 55.0 km/h, and 45.0 min at 35.0 km/h and spends 35.0 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

Answers

Explanation:Solution: Let the time be t1=35min = 0.58mint2=10min=0.166mint3=45min= 0.75mint4=35min= 0.58minlet the velocities bev1=100km/hv2=55km/hv3=35km/ha. Determine the average speed for the trip. km/hfirst we have to solve for the distanceS=s1+s2+s3S= v1t1+v2t2+v3t3S= 100*0.58+55*0.166+35*0.75S=58+9.13+26.25S=93.38kmV=S/t1+t2+t3+t4V=93.38/0.58+0.166+0.75+0.58V=93.38/2.076V=44.98km/hb. the distance is 93.38km

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