$\mathrm{}$ A freight train and a passenger train share the same rail track. The freight train leaves station A at $8$:$00$ A$.$M$.$ The train travels at a speed of $30$ mph for the first $10$ minutes and then continues to travel at a speed of $40$ mph$.$ At $8$:$35$ A$.$M$.,$ the passenger train leaves station A$.$ The passenger train travels first at a speed of $50$ mph for $5$ minutes and then continues to travel at a speed of $60$ mph$.$ Determine the location of the siding where the freight train will have to be parked to allow the faster passenger train to pass through. As a safety precaution, it is determined that the time headway between the two trains should not be allowed to fall below $5$ minutes