You drive on Interstate 10 from San Antonio to Houston, half thetime at 63 km/h

Question

You drive on Interstate 10 from San Antonio to Houston, half thetime at 63 km/h and the other half at73 km/h. On the way back you travel halfthe distance at 63 km/h and the other halfat 73 km/h. (a) What is your average speed from San Antonioto Houston?
km/h

(b) What is your average speed from Houston back to SanAntonio?
km/h

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

(d) What is your average velocity for the entire trip?
km/h

(a) What is your average speed from San Antonioto Houston?
km/h

(b) What is your average speed from Houston back to SanAntonio?
km/h

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

(d) What is your average velocity for the entire trip?
km/h

Explanation / Answer

. 01.   According to Google Directions, the distancebetween San Antonio and Houston is 197.32 miles. 02.   1 mile = 1.609344kilometers   ;   conversionfactor 03.   197.32 miles = 317.556 kilometers . 04.   Part a: 05.   (t/2)*63km/h + (t/2)*73km/h = 317.556km   ;   solve for t 06.   t = (317.556 km)/[(63km/h/2) + (73km/h/2)] =4.67 hours 07.   average speed = (317.556 km)/(4.67 hours) =68km/h . 08.   Part b: 09.   t1 = [(317.556 km)/(2)]/(63km/h) =(158.778km)/(63km/h) = 2.5203 hours 10.   t2 = [(317.556 km)/(2)]/(73km/h) =(158.778km)/(73km/h) = 2.1750 hours 11.   average speed = (317.556 km)/[(2.5203hours)+(2.1750 hours)] = 67.632km/h . 12.   Part c: 13.   average speed for the trip = (68.000km/h +67.632km/h)/(2) = 67.816km/h . 14.   Part d: 15.   Assume the direction from San Antonio toHouston is positive, and the direction from Houston to San Antoniois negative. 16.   average velocity = (+68.000km/h-67.632km/h)/(2) = +0.184km/h .

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