Question

a and b are two stations 350 k.m apart. a train starts from a at 7 am and travels towards b at 40 km per hour. another train starts from b at 8 a.m and travels towards a at 60k.m per hr.at what time do they meet?

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{trains}\mathrm{meet}\mathrm{after}\mathrm{t}\mathrm{hours}\mathrm{from}8\mathrm{am} \\ \mathrm{Distance}\mathrm{travelled}\mathrm{by}\mathrm{train}\mathrm{a}\mathrm{in}\mathrm{t}\mathrm{hours}=\mathrm{speed}\times \mathrm{time}=40\left(\mathrm{t}+1\right) \\ \mathrm{Distance}\mathrm{travelled}\mathrm{by}\mathrm{train}\mathrm{b}\mathrm{in}\mathrm{t}\mathrm{hours}=\mathrm{speed}\times \mathrm{time}=60\mathrm{t} \\ \mathrm{Total}\mathrm{distance}\mathrm{covered}\mathrm{by}\mathrm{both}\mathrm{the}\mathrm{trains}=350\mathrm{km} \\ 40\left(\mathrm{t}+1\right)+60\mathrm{t}=350 \\ \Rightarrow 40\mathrm{t}+40+60\mathrm{t}=350 \\ \Rightarrow 100\mathrm{t}=310 \\ \Rightarrow \mathrm{t}=3.1\mathrm{hours}=3\mathrm{hours}6\mathrm{minutes} \\ \mathrm{So}.\mathrm{train}\mathrm{meets}\mathrm{after}3\mathrm{hours}6\mathrm{minutes}\mathrm{from}11\mathrm{am} \end{gathered}$$
Regards