Car

The car goes from point A to point B at speed 86 km/h and back 53 km/h. If it goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is the distance between points A and B?

Correct result:

s =  258.4 km

Solution:

$$\begin{gathered} t_1=t_2+{\displaystyle \frac{10}{60}} \\ {\displaystyle \frac{s}{86}}+{\displaystyle \frac{s}{53}}={\displaystyle \frac{2s}{67}}+{\displaystyle \frac{10}{60}} \\ s={\displaystyle \frac{10}{60({\displaystyle \frac{1}{86}}+{\displaystyle \frac{1}{53}}-{\displaystyle \frac{2}{67}})}} \\ s=258.4\text{ km} \end{gathered}$$

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