Really need help..I can't figure out how?

A van travelling at 60km/h left Town A for Town B at 7.00am. At 7.30am, a car left Town A for Town B. If the car travelled at an average speed of 80km/h, at what time would it catch up with the van?

When the car catches up with the van, they would have both traveled the same distance

let the time from 7:30 am to the catch-up time be t hrs.
distance covered by car = 80t
distance covered by van = 60t + (1/2)(60)
= 60t + 30

80t = 60t + 30
20t = 30
t = 3/2
3/2 hours added to 7:30 am would make it 9:00 am

check:
the car went 80t
= 1.5 hrs at 80 km/h or 120 km

the van went 60t + 30
= (3/2)(60) + 30
= 120

To find out at what time the car would catch up with the van, we can use the concept of relative speed. The relative speed is the difference between the speeds of the car and the van.

Given:
- Van speed = 60 km/h
- Car speed = 80 km/h

To find the relative speed of the car and the van, we subtract the van speed from the car speed:
Relative speed = Car speed - Van speed = 80 km/h - 60 km/h = 20 km/h

Now, we need to determine the time it takes for the car to catch up with the van. Since the car started 30 minutes (0.5 hours) after the van, we need to calculate the distance covered by the van during that time.

Distance covered by the van in 0.5 hours = Van speed × Time = 60 km/h × 0.5 h = 30 km

Now that we know the van has a head start of 30 km, we can consider the scenario as if the car started from 30 km behind the van at the same time.

To find the time it takes for the car to catch up with the van, we use the formula:
Time = Distance / Relative speed

Time = 30 km / 20 km/h = 1.5 hours

Since the car journey started at 7.30 am, it would take 1.5 hours to catch up with the van. Therefore, the time the car would catch up with the van is 7.30 am + 1.5 hours = 9.00 am.