Distance between two cities

The car went from A to B in 4 hours. The car was up 15 km/h faster on the way back. The return trip took 48 minutes shorter than the way there. Find the distance of cities A and B.

Final Answer:

x =  240 km

Step-by-step explanation:

$$\begin{gathered} t_1=4\text{h} \\ \Delta t=\frac{48}{60}=\frac{4}{5}=0.8\text{h} \\ {t}_2=t_1-\Delta t=4-0.8=\frac{16}{5}=3.2\text{h} \\ x=v\cdot t_1 \\ x=(v+15)\cdot t_2 \\ v\cdot t_1=(v+15)\cdot t_2 \\ v\cdot 4=(v+15)\cdot 3.2 \\ 0.8v=48 \\ v=\frac{48}{0.8}=60 \\ v=60 \\ x=v\cdot t_1=60\cdot 4=240\text{km} \end{gathered}$$

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