Question

A man travels one - third of his journey with a speed of 40 km/h, half of the remaining distance with a speed of 20 km/h. if the average speed of the journey is 25km/hr and the total distance travelled is 135 km, find the time and speed taken during the last part of his journey.

Answer 1

Answer:

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Answer 2

Answer:

Total time = 5.4 hrs and Speed of the last journey = 22.22km/hr

Explanation:

Given , total distance = 135 km

Average speed = 25km/hr

A man travels $\frac{1}{3}$ of his journey with speed = 40 km/hr

So , distance = $\frac{135}{3} = 45$ km .

Time ($t_1$) = $\frac{distance }{ speed }$ = $\frac{45}{40 } = 1.125$ hr .

Therefore , the  total remaining distance = 135 - 45 = 90km

And half of the remaining distance cover with speed = 20km/hr .

So , distance =  45km

Then time ($t_2$) = $\frac{distance }{speed } = \frac{45}{20} = 2.25$ hr

Now , the  distance of his last part of journey    =  45km  

As we know that ,

Average speed = $\frac{total \ distance }{total \ time }$

⇒ Total Time = $\frac{ distance }{ average \ speed } = \frac{135}{25}$  = 5.4 hr

So , the total time he take to complete the journey = 5.4 hr.

Therefore , time for the last part of his journey  $t_3 = T - (t_1 + t_2)$

[Where T stand for total time taken }

⇒$t_3 = 5.4 -(1.125 + 2.25)$   [∴ T = 5.4 hrs , $t_1 = 1.125 hr \ and\ t_2 = 2.25hr$]

⇒$t_3 = 2.025$ hr

Therefore , the speed of the last part of his journey.

Speed = $\frac{45 }{2.025}$ = 22.22km/hr

Hence , total time is 5.4 hr and speed taken during the last part of his journey is 22.22km/hr .

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