At 11:00am a car (1) leaves city "A" at a constant rate of 60 mi/hr toward city "B". AT the same time a second car (2) leaves city "A" at the constant rate of 50 mi/hr. The distance between cities A and B is 220miles and a highway used by the two cars connects these cities. At what time will the two cars cross eachother?
I think it will be at three tweenty because it will take car (1) will get in the middle of the cities in 4hrs. and car two will get three in 4hrs. 40min. so I added the two together and divided by two and got 3:20 p.m.
To find the time at which the two cars cross each other, we need to determine the time it takes for each car to travel a certain distance.
Let's first find the equation for the distance traveled by each car. We know that distance = rate × time (i.e., d = rt).
For the first car, the distance traveled is given by:
d1 = r1 × t
Similarly, for the second car, the distance traveled is given by:
d2 = r2 × t
Since they start at the same time, the total distance between the two cars will be equal to the sum of the distances traveled by both cars:
d1 + d2 = 220 (total distance)
Substituting the values:
60t + 50t = 220
Combining like terms:
110t = 220
Dividing both sides by 110:
t = 2
Therefore, it will take 2 hours for the two cars to cross each other. To find the time of crossing, we add 2 hours to the starting time.
Starting Time: 11:00 am
Crossing Time: 11:00 am + 2 hours = 1:00 pm
So, the two cars will cross each other at 1:00 pm.
To find out at what time the two cars will cross each other, we need to consider their rates of travel and the distance between the cities.
Car 1 is traveling at a rate of 60 miles per hour, and Car 2 is traveling at a rate of 50 miles per hour. Since they both leave city A at the same time, their relative speeds can be calculated by subtracting the speed of Car 2 from the speed of Car 1.
Relative speed = Speed of Car 1 - Speed of Car 2
Relative speed = 60 mph - 50 mph
Relative speed = 10 mph
The distance between cities A and B is 220 miles. To determine when the two cars will cross each other, we divide the distance by their relative speed.
Time = Distance / Relative speed
Time = 220 miles / 10 mph
Time = 22 hours
Therefore, the two cars will cross each other after 22 hours. However, this answer seems unusually long, so let's check our calculations.
Upon closer inspection, it seems there is an error in the problem statement. The relative speed of the two cars is actually the sum of their individual speeds, since they are traveling towards each other.
Relative speed = Speed of Car 1 + Speed of Car 2
Relative speed = 60 mph + 50 mph
Relative speed = 110 mph
Now, let's recalculate the time using the corrected relative speed.
Time = Distance / Relative speed
Time = 220 miles / 110 mph
Time = 2 hours
Therefore, the two cars will cross each other after 2 hours, or at 1:00pm.