Question

A car travels, 40 km at a uniform speed of 40 kmh^-1 What should be its speed for the next 80 km if the average speed of the journey is 60 kmph

Answer 1

Step 1: Diagram

Step 2: Given data

Distance AB X₁= 40 km

Distance BC X₂ =80 km

Total distance X=$80km+40km=120km$

Uniform speed for the 40 km V₁=40 km h^-1

speed for the 80 km V₂ =?

Average speed From A to C = 60 km h^-1

Step 3: Calculation

Speed is defined as the ratio of distance traveled per total time taken.

$Speed=\frac{dis\tan ce}{timetaken}$

so,

$Timetaken=\frac{distnce}{speed}$

From A to B,

$Timetaken,t_1=\frac{dis\tan ce}{speed}=\frac{40}{40}=1hr$

From B to C,

$Timetaken{t}_2=\frac{80}{v_2}$

Total time $T=t_1+t_2$

We know that,

$$\begin{gathered} Averagespeed=\frac{Totaldis\tan ce}{Totaltimetaken} \\ 60=\frac{120}{t_1+t_2} \\ 60=\frac{120}{1+{\displaystyle \frac{80}{v_2}}} \\ 60=\frac{120}{{\displaystyle \frac{v_2+80}{v_2}}} \\ 60\left(\frac{v_2+80}{v_2}\right)=120 \\ 60(1+\frac{80}{v_2})=120 \\ 60+\frac{4800}{v_2}=120 \\ \frac{4800}{v_2}=120-60 \\ =60 \\ {v}_2=\frac{4800}{60}=80\frac{km}{hr} \end{gathered}$$

Hence,

The speed for the 80 km is 80 km h^-1