A truck left midville at 2:00 p.m. for Carmine, traveling at 40 mil/hr. At 3:15 p.m. a car left Carmine for Midville at 55 mi/hr. The truck and car passed each other exactly 2 hours before the car reached Midville. How far is it from Midville to Carmine?
Can someone please help me?
Thank you.
Midville.........................Carmine
distance = X
truck..............|...............Car
truck moves 40 mph*1.25 hrs = 50 miles
The car moves from carmine to 110 miles out(55 mph x 2 hrs = 110 miles)
Therefore, the truck moves from 50 miles out of Midville while the car moves from Carmine to the 110 mile spot. The truck moved 60 miles in that time frame.
Distance = rate x time
truck moved 60 miles @ 40 mph or 1.5 hours. The car moved X-110 in that same time of 1.5 hrs so
(X-110)/55 = 1.5 hrs.
Solve for X.
Check me out on that. It looks ok to me. Hopefully one of the math guys will check this.
clearly the vehicles met 110 miles from Midville.
At 40mi/hr, it took the truck 1:22.5 to cover that distance. So, the vehicles met at 2:00 + 1:22.5 = 3:22.5
The car had only been going for 7.5 minutes, covering only 6.875 miles.
So, the towns are 116.875 miles apart.
At 40 mph doesn't it take the truck 110/40 = 2.75 hours to cover that distance?
hmmm. yeah. I wonder how I
(a) got that answer, and
(b) didn't immediately notice that it made no sense.
Anyway, Rachel, you can see how to fix it and get the right answer. Unlike me, check it for consistency!
This is really old but it seems this is not cleared so.....
To find the distance from Midville to where the car and truck met. We can use the cars speed and knowing that it took 2 hours to get cover that distance.
D = R x T, and the time was 2 hours going at 55 mph so we get 110 miles.
Now lets represent that in terms of the truck. Thee truck left 1 and 1/4 hour earlier than the other car and got to the meetup spot. We can represent the unknown time as 't'. D = R x T, so 110 = 40 x (t + 5/4).
Divide both sides by 40 and you get (t+5/4) = 11/4. Sub 5/4 from both sides and you get t = 6/4 = 3/2. 3/2 is the time to travel the other distance from Carmine to the meeting spot. If we add that to the distance from Midville to the meeting spot we have 110 + 3/2 * 55 = 192.5.
The distance from Midville to Carmine is 192.5 miles.
Sure, I'd be happy to help!
To solve this problem, we can use a simple equation based on the information given. Let's break down the information step by step:
1. The truck left Midville at 2:00 p.m. and traveled at 40 miles per hour. This means that by the time the car left Carmine at 3:15 p.m., the truck had already been on the road for 1 hour and 15 minutes (or 1.25 hours).
2. It is stated that the truck and car passed each other exactly 2 hours before the car reached Midville. This means that the car was on the road for 2 hours longer than the truck when they passed each other.
3. We know that the car was traveling at 55 miles per hour throughout its entire journey.
Now, let's calculate the time it took for the truck to reach the point of passing:
Distance traveled by the truck = Speed of the truck × Time taken by the truck
Distance traveled by the truck = 40 miles per hour × 1.25 hours
Distance traveled by the truck = 50 miles
Since the car was on the road for 2 hours longer than the truck when they passed each other, we can subtract 2 hours from the time the car took to reach Midville:
Time taken by the car = Time taken to reach Midville - 2 hours
Time taken by the car = (2:00 p.m. to 3:15 p.m.) - 2 hours
Time taken by the car = 1.25 hours - 2 hours
Time taken by the car = -0.75 hours
However, the negative value doesn't make sense in this context, so we need to consider the absolute value:
Absolute value of -0.75 hours = 0.75 hours
Since we know the car traveled at a constant speed of 55 miles per hour throughout its entire journey, we can calculate the distance from Carmine to Midville:
Distance traveled by the car = Speed of the car × Time taken by the car
Distance traveled by the car = 55 miles per hour × 0.75 hours
Distance traveled by the car = 41.25 miles
Therefore, the distance from Midville to Carmine is approximately 41.25 miles.