Answer:
a) 2:15 pm
b) 240 km
Explanation:
You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.
Head start
The van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.
Closing speed
The speed at which that distance is reduced is the difference between the car speed and the van speed:
80 km/h -64 km/h = 16 km/h
Closing time
The time it takes for the head-start distance to be reduced to zero is ...
time = distance/speed
time = (48 km)/(16 km/h) = 3 h
a) Meeting time
Three hours after the car leaves, it will catch up with the van. That time is ... 11:15 +3:00 = 14:15 = 2:15 p.m.
b) Meeting distance
In 3 hours, the car travels (3 h)(80 km/h) = 240 km.
Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.
__
Additional comment
The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.