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Matter In Our Surroundings

Question
CBSEENSC9005712

A car travels a certain distance with a speed of 50 km/h and returns with a speed of 40 km/h. Calculate the average speed for the whole journey.

Solution

Let the car travel one way distance of x km.
S p e e d space o f space c a r space i n space t h e space f o r w a r d space j o u r n e y space equals space 50 space k m divided by h r

S o comma space t i m e space t a k e n space equals fraction numerator D i s tan c e space over denominator S p e e d end fraction equals x over 50 h space

S p e e d space o f space c a r space i n space t h e space r e t u r n space j o u r n e y space equals space 40 space k m divided by h r

T i m e space t a k e n space i n space t h e space r e t u r n space j o u r n e y space equals space straight x over 40 straight h
Total space time space for space the space whole space journey space equals space straight x over 50 plus straight x over 40 equals fraction numerator 4 straight x plus 5 straight x over denominator 200 end fraction equals fraction numerator 9 straight x over denominator 200 end fraction straight h

Total space distance space covered space equals space straight x space plus space straight x space equals space 2 straight x space km

therefore space space space space Average space speed space equals fraction numerator Total space distance over denominator Total space time end fraction

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals fraction numerator 2 straight x over denominator begin display style fraction numerator 9 straight x over denominator 200 end fraction end style end fraction space equals fraction numerator 2 straight x space cross times space 200 over denominator 9 straight x end fraction

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 400 over 9 equals 44.44 space km divided by straight h.