A woman driving a care 14ft long is passing a truck 30 ft long. The truck is traveling at 50 miles per hour. How fast must the woman drive her car so that she can pass the truck completely in 6 seconds?
Assume the truck is standing still, then she must travel a total distance of (14+30)ft in 6 seconds
speed = distance/time = 44 ft/6 sec
44 ft/6 sec = 440 ft/60 sec
= 440 ft/min = 26400 ft/hr
= 5 mi/hr
So she must travel 5 mph faster than the truck, which was going at 50 mph
So she will have to travel 60 mph
To find the speed at which the woman must drive her car in order to pass the truck completely in 6 seconds, we need to determine the relative speed between the two vehicles.
First, let's convert the length of the car and truck from feet to miles. There are 5,280 feet in a mile, so the car is 14 feet long, which is approximately 0.00265 miles (14/5280). Similarly, the truck is 30 feet long, which is approximately 0.00568 miles (30/5280).
Since the woman wants to pass the truck completely, she needs to cover a distance equal to the sum of the lengths of the truck and car, which is approximately 0.00833 miles (0.00265 + 0.00568).
Now, we can determine the speed required to cover this distance in 6 seconds. Divide the distance by the time to get the speed: 0.00833 miles / 6 seconds = approximately 0.00139 miles per second.
To convert this speed from seconds to hours, multiply by 3600 (the number of seconds in an hour): 0.00139 miles per second * 3600 seconds per hour = approximately 5 miles per hour.
Therefore, the woman must drive her car at a speed of approximately 5 miles per hour faster than the truck's speed to pass it completely in 6 seconds.