you drive on interstate 10 from San Antonio to Houston, half the time at 55 km/h and the other half at 90 km/h. On the way back you travel half the distance at 55 km/h and the other half at 90 km/h. What is your average speed from (a) San Antonio to Houston, (b) Houston to San Antonio?
Answers
Answer:
The average speed from (a) San Antonio to Houston is 72.5 km/h
(b) Houston to San Antonio is 68.27 km/h
Explanation:
According to the problem while going to Houston the the half of the time the speed was 55 km/h and next half of the time was 90 km/h
While coming back on the first half the speed was 55 km/h and on the next half the speed was 90 km/h
a) Therefore the average speed is given by
S(avg) = total distance / t
Now total distance, s = u1x t/2 +u2 x t/2
where u1 = 55 km/hr and u2 = 90 km/hr
Therefore S(avg) = u1x t/2 +u2 x t/2 /t
= (t/2)(u1+u2)/t
= u1+u2/2
= 55+90/2 = 72.5 km/h
b) Therefore the average speed is given by
S(avg) = total distance/t
Now total distance is P
S(avg) = P/t1+t2
where t1 is the time taken for the displacement at u1 speed and t2 is for u2
we can write ,
t1 = p1/u1 = P/2/v1 and t2 = p2/u2 = P/2/u2
Therefore S(avg) = P/t1+t2
= P/P/2/u1+ P/2/u2
= 1/2x 55 + 2 x 90
= 68.27 km/h