Question

4.
A cyclist goes from a place to another and returns by the same route. He pedals
his way uni-formly with speed U while going and with speed V while returning. The
average speed of his journey is:​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

GIVEN

A cyclist goes from a place to another and returns by the same route. He pedals his way uni-formly with speed U while going and with speed V while returning

TO DETERMINE

The average speed of his journey

CALCULATION

Let the starting place is A and the destination point is B

Let s be the distance between the point

Also let the cyclist takes time t to travel from A to B and takes time T to travel from B to A

So total distance covered = s + s = 2s

Total time taken = t + T

$\displaystyle \sf{ \: }Average \: Speed = \frac{Total \: Distance \: covered }{Total \: Time \: taken} \:$

$\implies \: \displaystyle \sf{ \: }Average \: Speed = \frac{2s }{t + T} \:$

Now the cyclist pedals his way from A to B uniformly with speed U

$\displaystyle \sf{ \: }t= \frac{s}{U}$

Again the cyclist pedals his way from B to S uniformly with speed V

SO

$\displaystyle \sf{ \: }T = \frac{s}{V}$

Hence

$\displaystyle \sf{ \: }Average \: Speed = \frac{2s }{t + T} \:$

$\displaystyle \sf{ \: }= \frac{2s }{ \frac{s}{U} + \frac{s}{V} } \:$

$\displaystyle \sf{ \: }= \frac{2 }{ \frac{1}{U} + \frac{1}{V} } \:$

$\displaystyle \sf{ \: }= \frac{2 \: {U} {V} }{ {U} + {V} } \:$

RESULT

$\boxed{ \: \displaystyle \sf{ \: }Average \: Speed = \: \:\frac{2 \: {U} {V} }{ {U} + {V} } \: }$

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LEARN MORE FROM BRAINLY

The ratio of the speed of two trains A and B running in the opposite direction is 5 : 15 . If each train is 200 m long and crosses each other in 10 s, then find the amount of time (in seconds) that train A takes to cross a man standing on a platform

https://brainly.in/question/23293703

Answer 2

Step-by-step explanation:

\displaystyle\huge\red{\underline{\underline{Solution}}}

Solution

GIVEN

A cyclist goes from a place to another and returns by the same route. He pedals his way uni-formly with speed U while going and with speed V while returning

TO DETERMINE

The average speed of his journey

CALCULATION

Let the starting place is A and the destination point is B

Let s be the distance between the point

Also let the cyclist takes time t to travel from A to B and takes time T to travel from B to A

So total distance covered = s + s = 2s

Total time taken = t + T

\displaystyle \sf{ \: }Average \: Speed = \frac{Total \: Distance \: covered }{Total \: Time \: taken} \:AverageSpeed=

TotalTimetaken

TotalDistancecovered

\implies \: \displaystyle \sf{ \: }Average \: Speed = \frac{2s }{t + T} \:⟹AverageSpeed=

t+T

2s

Now the cyclist pedals his way from A to B uniformly with speed U

\displaystyle \sf{ \: }t= \frac{s}{U}t=

U

s

Again the cyclist pedals his way from B to S uniformly with speed V

SO

\displaystyle \sf{ \: }T = \frac{s}{V}T=

V

s

Hence

\displaystyle \sf{ \: }Average \: Speed = \frac{2s }{t + T} \:AverageSpeed=

t+T

2s

\displaystyle \sf{ \: }= \frac{2s }{ \frac{s}{U} + \frac{s}{V} } \:=

U

s

+ V

s2s

\displaystyle \sf{ \: }= \frac{2 }{ \frac{1}{U} + \frac{1}{V} } \:=U1 + V12

\displaystyle \sf{ \: }= \frac{2 \: {U} {V} }{ {U} + {V} } \:=

U+V

2UV

RESULT

\boxed{ \: \displaystyle \sf{ \: }Average \: Speed = \: \:\frac{2 \: {U} {V} }{ {U} + {V} } \: }

AverageSpeed=

U+V

2UV

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

The ratio of the speed of two trains A and B running in the opposite direction is 5 : 15 . If each train is 200 m long and crosses each other in 10 s, then find the amount of time (in seconds) that train A takes to cross a man standing on a platform

https://brainly.in/question/23293703