at noon, a cargo van crosses an intersection at 30 mph. At 12:30 pm, a car crosses the same intersection traveling in the opposite direction. At 1 pm, the van and car are 54 miles apart. How fast is the car traveling?

I know the answer is 48 mph, but can you set it up for me?

Let's do it by logic and you set it up.
The van traveled for 1 hour at 30 mph so it will travel 30 miles.
At the end of 1 hour, the van and car were 54 miles apart; therefore, the van has traveled 54-30 = 24 miles.
The van traveled 24 miles in 1/2 hour which is 48 miles in 1 hour.

I hope the gets you started.

Sure! Let's set up the problem using the information given.

Let's assume that the car is traveling at a speed of x mph.

The cargo van travels at a speed of 30 mph and crosses the intersection at noon. It has been traveling for 1 hour by 1 pm, so it has covered a distance of 30 miles (30 mph * 1 hour = 30 miles).

At 12:30 pm, the car crosses the same intersection and starts moving in the opposite direction. At this point, the van and car start moving away from each other.

By 1 pm, they are 54 miles apart. This means that the combined distance traveled by the van and car is 54 miles.

Let's calculate the distance traveled by the car. Since we know the distance traveled by the van is 30 miles, we can subtract this from the total distance of 54 miles.

Distance traveled by the car = Total distance - Distance traveled by the van
Distance traveled by the car = 54 miles - 30 miles
Distance traveled by the car = 24 miles

Now, we know that the car has traveled 24 miles in 1/2 hour. To find its speed in miles per hour (mph), we need to convert the time from half an hour to one hour.

Speed of the car = Distance traveled by the car / Time taken by the car
Speed of the car = 24 miles / 0.5 hour
Speed of the car = 48 miles per hour (mph)

Therefore, the car is traveling at a speed of 48 mph.