I have figured the equation for this word problem Train A is traveling parallel to Train B. Train A is traveling at 100 mph and Train B at 110 mph Train A passes a station at 1:15pm Train B passes the same station at 1:45pm When will Train B catch up with Train A? I have 100*t=110(t-1/2) then t=110t-55 so t=11/2 and now I am stuck could someone help me out here?
Sure, I can help you with that. You have made a good start in setting up the equation based on the information given in the word problem. Let's go through it step by step to find out when Train B will catch up with Train A.
First, let's assign variables to the unknowns:
Let t represent the time it takes for Train B to catch up with Train A.
Now, let's set up the equation based on the information provided:
Train A travels at a rate of 100 mph and Train B travels at a rate of 110 mph. As Train B starts 30 minutes (or 1/2 hour) after Train A, we can say that Train A has been traveling for t hours and Train B has been traveling for (t-1/2) hours.
Since distance = speed × time, we can say that the distance traveled by Train A in t hours is 100t, and the distance traveled by Train B in (t-1/2) hours is 110(t-1/2).
According to the problem, Train B catches up with Train A at the same location, which means the distances traveled by both trains are equal. Therefore, we can set up the equation:
100t = 110(t-1/2)
Now, let's continue solving the equation:
100t = 110t - 55
Subtract 110t from both sides:
-10t = -55
Divide both sides by -10:
t = -55 / -10
t = 5.5
So, the time it will take for Train B to catch up with Train A is 5.5 hours.
To find out when this will happen in terms of time on a clock, we need to add the starting time of Train A, which is 1:15pm. Train A passes the station at that time, so Train B will catch up with Train A at 1:15pm + 5.5 hours.
Adding 5.5 hours to 1:15pm, we get:
1:15pm + 5.5 hours = 6:45pm
Therefore, Train B will catch up with Train A at 6:45pm.