Train A leaves a station traveling at 80km/h. Two hours later, train B leaves the same direction at 90km/h. How long does it take train B to catch up to train A?
They will have traveled the same distance, but the difference is their times will be 2 hours
time for slower train = D/80
time for faster train = D/90
D/80 - D/90 = 2
times 720
9D - 8D = 1440
D = 1440
Time for train B (the faster) = 1440/90 = 16 hrs.
check:
in 16 hrs, the faster train goes 16(90) = 1440
in 18 hrs, the slower train goes 18(80) = 1440
yeahhh!
To find out how long it takes for train B to catch up to train A, we can use the concept of relative speed.
First, let's determine the head start distance that train A has traveled during the two-hour gap. Since train A is moving at a constant speed of 80 km/h, and it leaves two hours earlier, its head start distance would be:
Head start distance (A) = Speed (A) * Time (A)
= 80 km/h * 2 hours
= 160 km
Now, we can consider the relative speed between the two trains. Train B is moving at 90 km/h, which is 10 km/h faster than train A. This means that train B is gaining on train A at a relative speed of 10 km/h.
To catch up to the head start distance of 160 km, we can set up the equation:
Time (B) * Relative speed = Head start distance
Let's represent the time taken by train B to catch up as "t" in hours:
t hours * 10 km/h = 160 km
Solving this equation for "t" gives us:
t = 160 km / 10 km/h
t = 16 hours
Therefore, train B will take 16 hours to catch up to train A.