Ascent and descent

The car goes 114 km of track, consisting of ascent and descent at 1 hour 35 minutes. When climbing, it moves at the speed of 48 km/h and downhill at 25 m/s. What is the length of the climb and descent?

Final Answer:

a =  32.5714 km
b =  81.4286 km

Step-by-step explanation:

$$\begin{gathered} s=114\text{km} \\ {v}_1=48\text{km/h} \\ {v}_2=25\text{m/s}\to \text{km/h}=25\cdot 3.6\text{km/h}=90\text{km/h} \\ t=1:35=1hr35min=1+\frac{35}{60}=1.5833hr\doteq 1.5833 \\ s=vt=s_1+s_2 \\ a+b=s \\ a/v_1+b/v_2=t \\ a+b=114 \\ a/48+b/90=1.5833333333333 \\ a+b=114 \\ 15a+8b=1140 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{15}\cdot Row1\to Row2 \\ 0.47b=38 \\ b=\frac{38}{0.46666667}=81.42857143 \\ a=\frac{1140-8b}{15}=\frac{1140-8\cdot 81.42857143}{15}=32.57142857=32.5714\text{km} \\ a=\frac{228}{7}\doteq 32.571429 \\ b=\frac{570}{7}\doteq 81.428571 \end{gathered}$$

Try another example