Train a is traveling @ 60 miles per hour. Train b is traveling @ 80 miles per hour. A arrives @ 9:25 am and b arrives @ 9:40 am what ime will train b catch up to train a?
Do you not mean departs, not arrives? If so:
a travels 40-25 = 15 minutes longer than b
if b travels for t minutes, then a travels for t+15 minutes
a speed = 60/60 = 1 miles/min
b speed = 80/60 = 4/3 miles/min
distances are the same so
1(t+15) = (4/3) t
3 t + 45 = 4 t
t = 45 minutes
so time = 9:40 + 45 = 10:25 am
9:40am - 9:25am = 15min.
15min/60min/h = 0.25h.
When train "B" catches up,the distance
traveled will be the same for each train:
d1 = d2.
60(t+0.25) = 80t,
60t + 15 = 80t,
t = 0.75h = 45min = Time required for
"B" to catch-up.
Time = 9:40 + 45 = 10:25am.
To solve this problem, we need to find the time it takes for Train B to catch up to Train A. We can do this by setting up an equation using the distance, rate, and time.
Let's assume that both trains started at the same time and traveled the same distance when Train B catches up to Train A. Let's also assume that the time it takes for Train B to catch up is represented by 't' hours.
First, we need to find the head start that Train A had over Train B. Since Train A arrived at 9:25 am and Train B arrived at 9:40 am, Train A had a head start of 15 minutes, which is equivalent to 15/60 = 1/4 hour.
Now, let's calculate the distance each train traveled during the time it took for Train B to catch up to Train A.
Distance traveled by Train A = rate * time
Distance traveled by Train A = 60 * (t + 1/4)
Distance traveled by Train B = rate * time
Distance traveled by Train B = 80 * t
Since the distances traveled by both trains are equal when Train B catches up to Train A, we can set up an equation:
60 * (t + 1/4) = 80 * t
To solve this equation, we can distribute and simplify:
60t + 15 = 80t
Combine like terms:
15 = 80t - 60t
15 = 20t
Divide both sides by 20:
15/20 = t
3/4 = t
Therefore, it will take Train B 3/4 of an hour to catch up to Train A.
Now, let's find the exact time when Train B catches up to Train A. Since Train A arrived at 9:25 am, we add 3/4 of an hour to get the catch-up time:
9:25 am + 45 minutes = 10:10 am
So, Train B will catch up to Train A at 10:10 am.