some math question?

Question

Train 5 leaves a station traveling at 80 km/h. eight hours later, train B leaves the same station traveling in the same direction at 100 km/h. How long does it take train B to catch up to train A?

i don't get these moving problems
could someone please explain???????
please?????

ty in advance

Answer 1

Moving problems tend to be about things starting at different times and moving at different rates arriving in the same place or traveling a specified distance.
Then the question is: How much time? or How far?
Or what was the rate?

These are the questions that can come from the formula Dist. = Rate x Time

Set up the terms to balance the equation of one train with the equation of the other train.
Let X = Time and (8hr x 80miles) equal the head start.
then we want to know when the first train and second train will be equal (at the same place).
When the rate x time on one side of the equation for one train is balanced with the rate x time on the other side for the other train plus the head-start, it is easy to figure when the trains will be equal.
100x = 80x + (8 x 80)
100x = 80x + 640
20x = 640 . . . . . . . . x = 20/640 = 32 hours
It takes 32 hours for train #2 to catch up to train #1.

Answer 2

Ok, heres how I got it.

8 hours after train A starts, B starts
The train is going at 80 km/hr for 8 hrs. 8 x 80 = 640 km
So this meanstrain A is 640 km ahead of train B when train B starts.

The rate of train A is 80 km/hr, the rate of train B is 100 km/hr

From this you can derive these equations:

640 + 80t = d
100t = d

100 and 80 being the rates, t being the time, and d the distance
The distances are equal in the problem and the equations so:

640 + 80t = 100t Now subtract by 80t on both sides...
640 = 20t Then Divide by 20.
32 = t

And there you go. It will take 32 hours before the two trains will meet.

Answer 3

Distance = rate * time

First train has traveled

D = 80 * 8 = 640 km when second train starts

Train B's rate is 100kmh, but the relative speed to A is only 20 kmh, since B's rate is 80 kmh

Since A was at 640 when B started

Distance = rate * time

640 = 20t

t = 32 hrs for B to catch A.
.

Answer 4

The answer is 32 hours.

Easiest way is to figure like this:
At 8 hours: Train A is 640 Miles ahead (80 miles X 8 hrs) and Train B is at 0 miles. So the question is how many hours will it take B to make up this 640 miles -- when it is traveling 25% faster than A (80mph + 25% = 100mph). To figure this, take the 640 and divide by the 25%. You get 2,560 miles. A will cover this 2,560 miles in 32 hours (i.e., 2,560 divided by 80mph = 32 hours). B will reach this same miles point, which will be 3,200 miles (i.e., 2,560 miles plus the 640 miles that A already covered) in 32 hours (i.e., 3,200 miles divided by 100mph).