A car traveling at an average speed of 55 kph leaves Town A for Town B, at a distance of 120 km. At the same time, another car, traveling on the same highway at an average speed of 45 kph, leaves Town B for Town A. How many hours will they meet? How far from Town A will they meet?
Their combined speed is 100 km/hr
distance = speed * time, so they will meet in
120/100 = 6/5 hours.
So, how far will A go in that time?
Let the distance from A to the meeting point be x km
then the distance from B to the meeting point is 120-x km
time from point A = x/55
time from point B = (120-x)/45
but those two times must be equal, they both left at the same time.
x/55 = (120-x)/45
cross-multiply
45x = 6600 - 55x
100x = 6600
x = 66
They will meet 66 km from town A
the time will be x/55 or 66/55 = 6/5 hrs
which is 1 hour and 12 minutes
(notice I would get the same time if I had used
(120-x)/45
= (120-66)/45
= 54/45
= 6/5
To find out how many hours the two cars will meet and the distance from Town A where they will meet, we can use the formula:
Time = Distance / Speed
Let's calculate the time it takes for each car to travel to the meeting point:
Car 1 (traveling from Town A to Town B):
Distance = 120 km
Speed = 55 kph
Time taken by Car 1 = Distance / Speed = 120 km / 55 kph
Car 2 (traveling from Town B to Town A):
Distance = 120 km
Speed = 45 kph
Time taken by Car 2 = Distance / Speed = 120 km / 45 kph
Since both cars are traveling at the same time, we can set the two times equal to each other:
120 km / 55 kph = 120 km / 45 kph
Now, we can solve for the time it takes for them to meet:
120 km / 55 kph = t hours
Cross-multiplying:
t = (120 km * 45 kph) / 55 kph
t = 98.18 hours
So, the two cars will meet approximately after 98.18 hours.
To calculate the distance from Town A where they will meet, we can multiply the speed of Car 1 by the time it takes for them to meet:
Distance = Speed * Time taken by Car 1 = 55 kph * 98.18 hours
Distance = 5399 km
Therefore, the two cars will meet after approximately 98.18 hours, and they will meet approximately 5399 km from Town A.