X and Y are two stations which are 320 miles apart. A train starts at a certain time from X and travels towards Y at 70 mph. After 2 hours, another train starts from Y and travels towards X at 20 mph. At what time do they meet?
Hoping they are on different tracks ..
Time taken by faster train til they meet --- t
time taken by slower train til they meet --- t-2
distance covered by faster train = 70t
distance covered by slower train = 20(t-2)
70t + 20(t-2) = 320
take over
70t + 20t - 40 = 320
70t + 20t = 320 - 40
90t = 280
t = 280/90
t = 3.11
NO, error from
70t + 20t - 40 = 320
to
70t + 20t = 320 - 40
should be 70t + 20t = 320 + 40
90t = 360
t = 4
To find the time when the two trains meet, we need to calculate the time taken by each train to cover the distance between the two stations.
Let's start with the train that starts from station X. It is traveling at a speed of 70 mph and has a head start of 2 hours. So, the distance covered by this train in the given time can be calculated using the formula:
Distance = Speed × Time
Distance = 70 mph × 2 hours
Distance = 140 miles
Now, we need to find out how much distance is left between the two trains after 2 hours. Since the total distance between the two stations is 320 miles, and the first train has already covered 140 miles, the remaining distance can be found by subtracting the distance covered by the first train from the total distance:
Remaining Distance = Total Distance - Distance Covered by First Train
Remaining Distance = 320 miles - 140 miles
Remaining Distance = 180 miles
Next, we need to calculate the time taken by the second train to cover this remaining distance. The second train is traveling at a speed of 20 mph. We can calculate the time using the same formula:
Time = Distance / Speed
Time = 180 miles / 20 mph
Time = 9 hours
Therefore, the two trains will meet after 9 hours from the time the second train starts. To calculate the total time when they meet, we add the 2-hour head start of the first train:
Total Time = Time taken by Second Train + Head Start of First Train
Total Time = 9 hours + 2 hours
Total Time = 11 hours
So, the two trains will meet after 11 hours from the time the first train starts from station X.