posted by Physics on .
can you show me how to do this mathematically
A car traveling 90 km/h is 100 m behind a truck traveling 75 km/h. How long will it take the car to reach the truck?
t r u c k xxxxxx|-------d---------|
The truck travels a distance, d km, while the car travels d + 0.100 km.
distance = rate x time. The time must be equal so
time = distance/rate
time for truck = d/75
time for car = (d+0.100)/90
time = time
d/75 = (d+0.100)/90
solve for d and I get 0.5 km. So the truck travels 0.5 km and the car travels 0.6 km. How long does that take.
d = r*t
t = d/r
t = 0.5/75 = 0.00667 hr or
t = 0.6/90 = 0.00667 hr.
You can convert 0.00667 hr to minutes, then to sec by
0.00667 hr x (60 min/hr) x (60 sec/min) = I get 24 seconds but check my work.
There is another way to do this which is a little shorter.
Note that the difference between 90 km/hr and 75 km/hr is 15 km/hr. So we ask ourselves how long it takes to cover that additional 0.1 km at the rate of 15 km/hr. That is t=d/r = 0.100/15 = 0.00667 hr. Voila!