Question

Toms home is 1800 m from his school. One morning he walked part of the way to school and then ran the rest. If it took him 20 minutes or less to get to school, and he walks at 70m/min and runs 210m/min, how far did he run?

Answer 1

`Formula\ for\ velocity\\\\ v=(s)/(t)\\\\s-distance\\\\ t-time\\\\ t=20min\\\\ v_1=70m/min\\\\v_2=210m/min\\\\s_1- distance\ when\ he\ walk \\\\s_2=distance\ when\ he\ run\\\\ s_1=1800-s_2\\\\`
`\left \{ {*t_1 \atop 210=(1800-s_1)/(20-t_1)\ \ \right. \\\\ \left\{{70*t_1=s_1}\atop{210(20-t_1)=1800-s_1}}\right\\\\ \left \{ {{70t_1=s_1} \atop {4200-210t_1=1800-s_1}} \right.\\\\ \left \{ {{70t_1=s_1} \atop {4200-1800=210t_1-s_1}} \right.\\\\ \left \{ {{70t_1=s_1} \atop {2400=210t_1-s_1}} \right.\\\\Substituting\ method:\\\\ 2400=210t_1-70t_1\\\\ 2400=140t_1\ \ |:140 t_1=(2400)/(140)=(240)/(14)=(120)/(7)=17(1)/(7)min\\\\t_2=2(6)/(7)min`
`s_2=v_2*t_2\\\\ s_2=210*2(6)/(7)\\\\ s_2=210*(20)/(7)=600m\\\\ He\ ran\ 600m\ or\ more.`