Dinesh 2

Dinesh left town L for town M at a constant speed and took 10 hours to complete the journey. At the same time, Saanvi left town M for town L, traveled at a constant speed, and took 6 hours to complete the journey. They both passed each other at a point 72 km from town L.

a) What is the distance between towns L and M?

b) What was Saanvi's speed for the whole journey?

Correct answer:

x =  192 km

Step-by-step explanation:

$$\begin{gathered} x_1=72\text{km} \\ x=x_1+x_2 \\ {t}_1=10\text{h} \\ {t}_2=6\text{h} \\ x=v_1\cdot t_1 \\ x=v_2\cdot t_2 \\ {x}_1=v_1\cdot t \\ x-x_1=v_2\cdot t \\ {x}_1=(x/t_1)\cdot t \\ x-x_1=(x/t_2)\cdot t \\ (x-x_1)/x_1=(x/t_2)/(x/t_1) \\ (x-x_1)/x_1=t_1/t_2 \\ x-x_1=x_1\cdot t_1/t_2 \\ x=x_1+x_1\cdot \frac{t_1}{t_2}=72+72\cdot \frac{10}{6}=192 \\ \text{ Verifying Solution: } \\ {v}_1=x/t_1=192/10=\frac{96}{5}=19.2\text{km/h} \\ {v}_2=x/t_2=192/6=32\text{km/h} \\ t=x_1/v_1=72/19.2=\frac{15}{4}=3.75\text{h} \\ {x}_2=x-x_1=192-72=120\text{km} \\ {T}_1=x/v_1=192/19.2=10\text{h} \\ {T}_2=x/v_2=192/32=6\text{h} \\ {T}_1=t_1,T_2=t_2 \\ {X}_1=v_1\cdot t=19.2\cdot 3.75=72\text{km} \\ {X}_2=v_2\cdot t=32\cdot 3.75=120\text{km} \\ {x}_1=X_1,x_2=X_2 \end{gathered}$$

Try another example