at 1p.m. two trains, traveling towards each other, leave from towns that are 312 km apart. one train averages at most 82 km/h and the other at most 74 km/h. what is the earliest time for them to meet?
when they meet they both will have travelled the same time after 1:00 pm
distance covered by faster train === x
distance covered by slower train == 312-x
time = distance/rate
x/82= (312-x)/74
solve for x
that will give you the distance, from there you can find the time
add that time to 1:00 pm
To find the earliest time for the two trains to meet, we need to calculate the time it takes for them to cover the distance of 312 km.
Let's assume that the two trains meet after a time 't' hours.
So, the distance covered by the first train in 't' hours will be (82 km/h) * t.
Similarly, the distance covered by the second train in 't' hours will be (74 km/h) * t.
Since they are traveling towards each other, the sum of the distances covered by both trains will be equal to the total distance of 312 km.
Therefore, we can write the equation:
(82 km/h) * t + (74 km/h) * t = 312 km
To find the earliest time, we need to solve this equation for 't'.
Combining like terms:
(82t + 74t) km/h = 312 km
156t km/h = 312 km
Dividing both sides by 156:
t = 312 km / 156 km/h
t = 2 hours
Therefore, the earliest time for the two trains to meet is 2 hours after they have started.
To find the earliest time for the two trains to meet, you need to calculate the time it takes for each train to cover the distance between them. Since they are traveling towards each other, their combined speeds will determine how quickly they meet.
Let's start by calculating the time it takes for the first train to travel the 312 km distance. The first train's speed is at most 82 km/h, so we can use the formula: time = distance / speed. Therefore, the time for the first train is 312 km / 82 km/h ≈ 3.81 hours.
Similarly, for the second train, we calculate the time it takes for it to travel 312 km at most 74 km/h. Using the same formula, we find the time for the second train is 312 km / 74 km/h ≈ 4.22 hours.
Since they are traveling towards each other, the earliest time for them to meet is determined by the slower train, which in this case is the train traveling at most 74 km/h. Therefore, the earliest meeting time is approximately 4.22 hours.
Taking the nearest whole number, the earliest time for the two trains to meet is 4 hours and 13 minutes after they both depart.