Question

A car travels first 30 km with a uniform speed of 60 km per hour and the next 30 km with a uniform speed of 40 km per hour calculate the total time of journey

Answer 1

Answer:

  V1 = 60km/hr D1 = 30 km

         T1 = ?

         V2 = 40 km /hr D2 = 30 km

         T2 = ?

Total Time = T1 + T2

We know that ,

           velocity = Distance /Time

Therefore ,

             V1 = D1/T1 or T1 = D1 / V1  => T1 = 30 km / 60 km /hr = 1/2 hr

              V2 = D2/T2 or T2 = D2/ V2  => T2 = 30 km / 40 km /hr = 3/4 hr

     Hence ,

               Total Time = T1 + T2 = 1/2 + 3/4 = 5/4 hrs

     we know that ,

               Average Velocity = Total Distance / total time taken = 30 + 30 / 5/4

                                         = 60/5/4 = 48 km /hr

Hence Average Velocity is 48km/hr and total time of journey = 5/4 hours.

My Short cut Method :-

           When a body travels equal distance with different velocities V1 and V2 , then Average Velocity is Calculated as

             Average Velocity = 2*V1*V2 / (V1 + V2 )

             here , V1 = 60 km/hr and V2 = 40 km/hr

     therefore ,

       Average Velocity = 2*60*40 / (60+40 )= 4800/100 = 48km/hr

Also we know that ,

           Average Velocity =  Total Distance / Total Time Taken

                     48 = 60 / Total Time Taken

               or Total Time Taken = 60/48 = 5/4 Hrs .

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Answer 2

Answer :-

$\boxed{ \sf{\: T= \frac{5}{4} \: hr \: \: or \: 75 \: minutes } \: } \:$

To Find :-

Total time of journey .

Explanation :-

Given that ;

$\implies \sf{V_{1} = 60 \: \frac{km}{hr} , D_{1} = 30 \: km \: } \\ \\ \therefore \sf{V_{1} = \frac{D_{1}}{T_{1} }} \\ \\ \to \sf{ 60 = \frac{30}{T_{1}} } \\ \\ \to \sf{T_{1} = \frac{30}{60} } \\ \\ \to \boxed{\sf{ T_{1} = \frac{1}{2} \: hr}}$

And ,

$\implies \: \sf{V_{2} = 40 \: \frac{km}{hr} , D_{1} = 30 \: km \: } \: \\ \\ \therefore \: \sf{V_{2} = \frac{D_{2}}{T_{2} }}\\ \\ \to \sf{ \: 40 = \frac{30}{T_{2} } } \\ \\ \to \boxed{\sf{ T_{2} = \frac{3}{4} \: hr}}$

hence,total time (T) is

$\implies \sf{T = T_{1} + T_{2}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{2} + \frac{3}{4} \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{2 + 3}{4} \\ \\ \: \: \: \: \: \: \: \: \: \boxed{ \sf{\: T= \frac{5}{4} \: hr \: \: or \: 75 \: minutes } \: }$

total time of journey is 75 minutes .