Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and train B is traveling at 60 miles per hour. Train A passes a station at 8:20pm. If train B passes at the same station at 8:35 p.m at what time will train B catch
up to train A.
when B gets to station, A is this far ahead:
distance: 1/4 hr*40mph= 10 miles.
So, to make up that 10 miles, B is traveling at a relative velocity of 20 mph (60-40)
time= distance/velocity= 10/20 hr
so, add that time, 30 min, to 8:35
In 1994, the life expectancy of males in a certain country was 73.8 years. In 2000, it was 77.4 years. Let E represent the life expectancy in year t and let t represent the number of years since 1994
To find out when train B will catch up to train A, we need to determine the time difference between their passes at the same station.
First, we need to find the time it takes for train A to travel from the station to the point where train B catches up to it. We can calculate this by using the formula:
Distance = Speed × Time
Since train A is traveling at 40 miles per hour, and the time is unknown, we'll substitute this into the formula:
Distance_A = 40 × Time_A
Next, we'll calculate the distance train B travels during the same time period. Train B travels 60 miles per hour, and the time it takes to catch up to train A is also unknown:
Distance_B = 60 × Time_B
Since both trains start from the same station, we know that the distance traveled by train A and train B will be the same when train B catches up to train A. Therefore, Distance_A = Distance_B. We can equate the two equations:
40 × Time_A = 60 × Time_B
Now, we need to determine the time difference between their passes at the station. Train A passes the station at 8:20 p.m and train B passes the station at 8:35 p.m.
The time difference is calculated by subtracting the earlier time from the later time:
Time_difference = 8:35 p.m - 8:20 p.m
Time_difference = 15 minutes
Now, we need to convert this 15-minute time difference into hours since we are dealing with speed in miles per hour. There are 60 minutes in one hour, so the conversion will be:
Time_difference_in_hours = 15 minutes / 60 minutes per hour
Time_difference_in_hours = 0.25 hours
Now, we can substitute the time difference into the equation we derived earlier:
40 × Time_A = 60 × Time_B
40 × Time_A = 60 × (Time_A + Time_difference_in_hours)
Solving this equation will give us the value of Time_A, which is the time train A will take to travel from the station to the point where train B catches up to it.
40 × Time_A = 60 × (Time_A + 0.25)
40 × Time_A = 60 × Time_A + 15
40 × Time_A - 60 × Time_A = 15
-20 × Time_A = 15
Dividing both sides by -20:
Time_A = 15 / -20
Time_A = -0.75 hours
Since time cannot be negative in this context, this solution is not valid. However, the negative value tells us that we need to add 0.75 hours to train A's pass time to find when train B catches up to it.
Adding 0.75 hours to 8:20 p.m:
8:20 p.m + 0.75 hours = 9:05 p.m
Therefore, train B will catch up to train A at 9:05 p.m.