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CBSE Class 9 Answered

Sam, while driving to school, computes the average speed for his trip to be 20 km/h. On his return trip along the same route, there is less traffic and the average speed is 30 km/h. What is the average speed for Sam’s trip?
Asked by Topperlearning User | 10 Jun, 2016, 10:51: AM
answered-by-expert Expert Answer

We need to calculate the time taken in each of the trip. After that, we can calculate the average speed.

Let the distance of the school = s km

Let time to reach the school in first trip = t1

Let time to reach the school in second trip = t2

begin mathsize 12px style We space know space that space average space speed equals fraction numerator Total space distance over denominator Total space time end fraction
For space the space first space trip colon space Average space speed equals fraction numerator Total space distance over denominator Total space time end fraction equals straight s over straight t subscript 1
rightwards arrow 20 space kmh to the power of negative 1 end exponent equals straight s over straight t subscript 1
rightwards arrow straight t subscript 1 equals straight s over 20 straight h
For space the space second space trip colon space Average space speed equals fraction numerator Total space distance over denominator Total space time end fraction equals straight s over straight t subscript 2
rightwards arrow 30 space kmh to the power of negative 1 end exponent equals straight s over straight t subscript 2
rightwards arrow straight t subscript 2 equals straight s over 30 straight h
Total space time space of space his space journey comma space straight t equals straight t subscript 1 plus straight t subscript 2 space equals straight s over 20 plus straight s over 30
rightwards arrow straight t equals straight s over 12 straight h space space........ space left parenthesis 1 right parenthesis
The space total space distance space of space his space whole space trip space is space apostrophe 2 straight s apostrophe.
Thus comma space average space speed space of space his space whole space trip space is space given space as
Average space speed equals fraction numerator Total space distance over denominator Total space time end fraction
rightwards arrow space space space space space space space space space space space space space space space space space space equals fraction numerator 2 straight s over denominator straight t end fraction space
rightwards arrow space space space space space space space space space space space space space space space space space space equals fraction numerator 2 straight s over denominator left parenthesis straight s divided by 12 right parenthesis end fraction
space Average space speed equals 24 space km divided by straight h space space space
end style

Therefore, average speed of Sam = 24 km/h

Answered by | 10 Jun, 2016, 12:51: PM
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