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You drive on Interstate 10 from San Antonio to Houston, one- half the time at 35.0 mi/h (= 56.3 km/h) and the other half at 55.0 mi/h (= 88.5 km/h). On the way back you travel one-half the distance at 35.0 mi/h and the other half at 55.0 mi/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?

You drive  on Interstate   10 from  San Antonio  to Houston,  one- half  the time at 35.0 mi/h  (= 56.3  km/h)  and the other  half at 55.0 mi/h  (= 88.5 km/h). On the way back you travel one-half the distance  at 35.0 mi/h  and the other half at 55.0 mi/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?

Grade:10

3 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
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Aparna Venkateshwaran
26 Points
6 years ago
Hi, I was solving this problem and I hit a snag in part c, where you say s is half the distance of s`. This implies s`=2s and not the other way around - won`t this change the answer for part c, because now a factor of 2 doesn`t cancel in one half of the denominator?
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

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