Take 8:00 to be the starting time, <em>t</em> = 0, and the car's starting position 20 km behind the truck to be the origin. Then the car's position at time <em>t</em> is
<em>x</em> = (70 km/h) <em>t</em>
and the truck's position is
<em>x</em> = 20 km + (58 km/h) <em>t</em>
<em />
(a) Right before the truck breaks down 0.5 h later, it will cover an additional distance of
(58 km/h) * (0.5 h) = 29 km
from its starting point, while the car will have covered a distance of
(70 km/h) * (0.5 h) = 35 km
from its starting point. So at 8:30, the truck is (20 km + 29 km) - 35 km = 14 km away from the car when it broke down.
(b) If neither vehicles stops, then the car passes the truck when their positions are equal, which would happen after
(70 km/h) <em>t</em> = 20 km + (58 km/h) <em>t</em>
(12 km/h) <em>t</em> = 20 km
<em>t</em> = (20 km) / (12 km/h)
<em>t</em> ≈ 1.7 h
But with the truck breaking down a 8:30, it is stuck 49 km away from the origin, so we need to find when the car travels this distance:
(70 km/h) <em>t</em> = 49 km
<em>t</em> = (49 km) / (70 km/h)
<em>t</em> = 0.7 h = 42 min
or at 8:42.
