Peleton

In a cycling race, the peloton travels at an average speed of 36 km/h. One competitor took 5 minutes to repair a puncture. How many kilometers per hour was his speed greater than the speed of the peloton when he caught up with him in 20 minutes? How long would it take him if the peloton immediately increased its speed to 40 km/h after the puncture?

Correct answer:

x =  9 km/h
t₃ =  40 min

Step-by-step explanation:

$$\begin{gathered} v_1=36\text{km/h} \\ {t}_1=5\text{min}\to \text{h}=5:60\text{h}=0.08333\text{h} \\ {t}_2=20\text{min}\to \text{h}=20:60\text{h}=0.33333\text{h} \\ {s}_1=s_2 \\ {v}_1\cdot (t_1+t_2)=(v_1+x)\cdot t_2 \\ x=v_1\cdot \frac{t_1+t_2}{t_2}-v_1=36\cdot \frac{0.0833+0.3333}{0.3333}-36=9\text{km/h} \end{gathered}$$

$$\begin{gathered} v_2=v_1+x=36+9=45\text{km/h} \\ {v}_3=40\text{km/h} \\ {s}_3=s_4 \\ {v}_3\cdot (t_1+y)=v_2\cdot y \\ 40\cdot (0.083333333333333+y)=45\cdot y \\ 5y=3.333333 \\ y=\frac{3.33333333}{5}=0.66666667 \\ y=\frac{2}{3}\doteq 0.666667 \\ {t}_3=y\to \text{min}=y\cdot 60\text{min}=0.6667\cdot 60\text{min}=40\text{min}=40\text{min} \end{gathered}$$

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