At 1 pm two trains, traveling toward each other leave from towns that are 312 km apart. One train averages at most 82km/h and the other at most 74km/h. What is the earliest possible time for them to meet?
Please help me solve this. I'm not exactly sure how to set up the equation or inequality.
i dont get it
Simplify please...thnks
X/50=(312-X)60
To solve this problem, we can set up an equation to represent the distance traveled by each train.
Let's call the time it takes for the trains to meet "t" hours.
The distance traveled by the first train is given by: d1 = (speed of the first train) * (time) = 82t km
The distance traveled by the second train is given by: d2 = (speed of the second train) * (time) = 74t km
Since the trains are traveling toward each other, the total distance they travel when they meet is equal to the distance between the towns, which is 312 km.
So, we can write the equation: d1 + d2 = 312
Substituting the expressions for d1 and d2, we have:
82t + 74t = 312
Now we can solve for t.
Combining like terms, we get:
156t = 312
Dividing both sides by 156:
t = 2
So, it will take 2 hours for the trains to meet.
To find the earliest possible time for them to meet, we need to know the starting times of each train. If one train leaves at exactly 1 pm, we need to calculate the starting time for the other train so that they meet at the earliest possible time.
Let's assume the second train leaves "x" hours after 1 pm. The first train will have traveled for "x + 2" hours when they meet.
Now, we calculate the distance traveled by each train in the time they traveled:
Distance traveled by the first train = 82 km/h * (x + 2) h
Distance traveled by the second train = 74 km/h * x h
Setting up the equation again:
82(x + 2) + 74x = 312
Now, we solve for x:
82x + 164 + 74x = 312
156x = 312 - 164
156x = 148
x = 148/156
x = 0.95 hours
Since time cannot be negative, and we are looking for the earliest possible time, we can round x up to 1 hour.
Therefore, the second train should leave 1 hour after 1 pm, which is at 2 pm, to meet the first train at the earliest possible time.
Thus, the earliest possible time for them to meet is 2 pm.
For these kind of questions you have to ask yourself,
which of my quantities are equal so I can make an equation?
When the meet, will they not have travelled the same time? So the times are equal
let the distance covered by the faster train be x km
then the distance covered by the slower train is 312-x km
time taken by faster train = x/82
time taken by slower train = (312-x)/72
so ..
x/82 = (312-x)/72
crossmultiply and simplify to get
x =166.13 km
so time is 166.13/82 = 2.026 hours