Question

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?

Answer 1

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