Ou drive on interstate 10 from san antonio to houston, half the time at 77 km/h and the other half at 119 km/h. on the way back you travel half the distance at 77 km/h and the other half at 119 km/h. what is your average speed (a) from san antonio to houston, (b) from houston back to san antonio, and (c) for the entire trip

Part a)98 km/h

Part b) 93.5 km/h

Part c) 95.7 km/h

Explanation:

A) For the trip from Antonio to Houston we have

Let the total time in which the trip is completed be 't'

Thus the distance covered with a speed of 77 km/h equals

Similarly the distance covered with a speed of 119 km/h equals

Now by definition of average speed we have

Average Speed =

Applying values we get

Average Speed for trip 1 =

Thus average speed equals

B)For the trip from Houston Antonio to we have

Let the total distance of the trip be 'd'

Time required to complete half the distance at a speed of 77 km/h equals

Time required to complete remaining half the distance at a speed of 119 km/h equals

Now by definition of average speed we have

Average Speed =

Applying values we get

Average Speed for trip 1 =

Thus average speed equals

C) For the entire trip we have

Average Speed =

Applying values we get

Average Speed for both the trips  =

Thus average speed for both the trips equals 95.7 km/h

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