Question

if a person walks at 4 meter/hr he covers a certain distance if he walks at 9 meter/hr he covers 7.5 miles more. How distance did he actually cover?

Answer 1

Let the time of motion of a person is $t$, then

$$d_1=v_1t/2$$

$$d_2=v_2t/2$$

Since

$$d_2=d_1+12070\:\rm m$$

we obtain

$$9\:\rm m/hr\times {\it t}/2=4\:\rm m/hr\times {\it t}/2+12070\: m$$

So the time of motion

$$t=2\times\frac{12070\:\rm m}{9\:\rm m/hr-4\:\rm m/hr}=4828\:\rm hr$$

The total distance

$$d=d_1+d_2$$

$$=4\:\rm m/hr\times4828/2\: hr+9\:\rm m/hr\times4828/2\: hr$$

$$=31382\: \rm m=19.5\: mi$$