A moving van leaves a house traveling at an average rate of 40mi/h. The family leaves 1/2 hour later following the same route in a car. They travel at an average of 60 mi/h.
and then stop for dinner?
If you want to know how long the car takes to overhaul the van, then since distance = speed * time, solve for t in
40t = 60(t - 1/2)
You might even want to find the distance, but I'll leave you to that.
Next time, proofread your post. Don't make us come up with the question as well as the answer!
Dv = Dc.
40*0.5 + 40*t = 60 * t.
t = 1hr. to catch up.
D = V*t = 60 * 1 = 60 miles traveled by each vehicle.
Ah, a moving van and a car engaged in a friendly race, huh? Well, buckle up and let's calculate the fun!
Since the moving van left half an hour earlier, it already has a head start. Now let's determine how much of a head start it got. We can use the formula:
Head Start = Speed × Time
For the moving van, the head start is 40 mi/h × 0.5 h = 20 miles. So, the van's already cruising 20 miles ahead of the family.
Now, let's find out when the family catches up to the van. We can use the same formula, but this time, let's replace the speed with relative speed, which is the difference in their speeds:
Relative Speed = Car Speed - Van Speed
Relative Speed = 60 mi/h - 40 mi/h = 20 mi/h
Now, dividing the head start (20 miles) by the relative speed (20 mi/h) tells us how long it takes for the family to catch up:
Time = Head Start / Relative Speed
Time = 20 miles / 20 mi/h
Time = 1 hour
So, after 1 hour of driving, the family will catch up with the moving van. I hope they have some amusing road trip games to pass the time!
To solve this problem, we can use the formula:
Distance = Speed x Time
Let's assume the distance between the house and the destination is D miles.
Step 1: Find the time it takes for the moving van to reach the destination.
The moving van is traveling at a speed of 40 mph. It leaves 1/2 hour earlier than the family, so the time it takes for the moving van to reach the destination is given by:
Time = D / 40
Step 2: Find the time it takes for the family to reach the destination.
The family is traveling at a speed of 60 mph. The time it takes for the family to reach the destination is:
Time = D / 60
Step 3: Find the difference in time between the moving van and the family.
The time difference is given by:
Time difference = Time taken by the moving van - Time taken by the family
= D / 40 - D / 60
Step 4: Simplify the expression for the time difference.
To simplify the expression, we need to find a common denominator:
Time difference = [(3D - 2D) / 120]
= D / 120
Therefore, the time difference between the moving van and the family is D / 120 hours, or D minutes.
Note: We have not been given the value of D, so we cannot find the exact time difference. However, we can see that the time difference is directly proportional to the distance D.
To find the time it takes for the family to catch up to the moving van, we can use the equation Distance = Rate × Time.
Let's assume the time it takes for the family to catch up to the moving van is represented by T (in hours).
Now, let's consider the distance the moving van covers during this time. Since the van starts half an hour earlier, it has a head start of 40 mi/h × (1/2) h = 20 miles.
During the time T, the moving van will travel at a rate of 40 mi/h for T + 1/2 hours.
So, the distance the moving van covers is Distance = Rate × Time = 40 mi/h × (T + 1/2) h.
Now, let's consider the distance the family covers during the same time T. The family is traveling at a rate of 60 mi/h for T hours.
So, the distance the family covers is Distance = Rate × Time = 60 mi/h × T h.
Since both the moving van and the family travel the same route, the distances they cover are the same:
40 mi/h × (T + 1/2) h = 60 mi/h × T h.
To solve for T, we can start by simplifying the equation:
40T + 20 = 60T.
Next, let's isolate T by bringing the terms with T to one side:
60T - 40T = 20.
Simplifying further:
20T = 20.
Dividing both sides by 20, we find:
T = 1.
Therefore, it takes the family 1 hour to catch up to the moving van.