Walking speeding

Susan walks from her home to office at 16 km/h, she is late by 5 min. If she walks by 20 km/h, she reaches 10 min before the office time. Find the distance of her office from her house.

Final Answer:

x =  20 km

Step-by-step explanation:

$$\begin{gathered} v_1=16\text{km/h} \\ {t}_1=5\text{min}\to \text{h}=5:60\text{h}=0.08333\text{h} \\ {v}_2=20\text{km/h} \\ {t}_2=10\text{min}\to \text{h}=10:60\text{h}=0.16667\text{h} \\ x=s_1=s_2 \\ x=v_1\cdot (t+t_1) \\ x=v_2\cdot (t-t_2) \\ {v}_1\cdot (t+t_1)=v_2\cdot (t-t_2) \\ 16\cdot (t+0.083333333333333)=20\cdot (t-0.16666666666667) \\ 4t=4.666667 \\ t=\frac{4.66666667}{4}=1.16666667 \\ t=\frac{7}{6}\doteq 1.166667 \\ x=v_1\cdot (t+t_1)=16\cdot (1.1667+0.0833)=20\text{km} \end{gathered}$$

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