Trains A and B are traveling in the same direction on parrallel tracks. Train A is traveling at 60 mph, and train B is traveling at 80 mph. Train A passes a station at 11:15 a.m. if train B passes the same station at 11:30 a.m. at what time will train B catch up to train A?
When will train B catch up to train A?
__:__ (a.m / p.m)
Translate into algebraic expression.
The product of 45% and some number.
Word problems are not my best quality,can someone please help me figure out the formula and how to solve this question>>> Thanks
To solve the first question, we need to determine the time difference between when Train A passes the station and when Train B passes the station.
We know that the distance traveled by both trains is the same when Train B catches up to Train A.
Let's consider the time it takes for Train B to catch up to Train A as 't' hours.
In 't' hours, Train A will have traveled a distance of 60t miles (since it is traveling at 60 mph).
Similarly, Train B will have traveled a distance of 80 (t - 15/60) miles (since it is traveling at 80 mph and started 15 minutes after Train A passed the station).
Since the distances traveled are equal, we can set up the equation:
60t = 80 (t - 15/60)
To solve for 't', let's simplify the equation:
60t = 80t - 20
20t = 20
t = 1
This means that it will take Train B 1 hour to catch up to Train A.
To find the exact time, we add 1 hour to the time when Train B passed the station, which is 11:30 a.m.
Therefore, Train B will catch up to Train A at 12:30 p.m.
Now, let's move on to the second question.
To translate the expression "the product of 45% and some number" into an algebraic expression, we can use the following:
Let the number be 'x'.
The product of 45% and 'x' can be written as 0.45x.
Therefore, the algebraic expression for "the product of 45% and some number" is 0.45x.
I hope this helps! Let me know if you have any further questions.
To solve the problem, we need to determine the time it takes for Train B to catch up to Train A.
Let's assume the time it takes for Train B to catch up to Train A is t hours after Train A passes the station.
In t hours, Train A travels a distance of 60t miles.
In t - 0.25 hours (which is 15 minutes less than t), Train B travels a distance of 80(t - 0.25) miles.
Since both trains are traveling the same distance when Train B catches up to Train A, we can set up the equation:
60t = 80(t - 0.25)
Now, let's solve this equation for t:
60t = 80t - 20
20t = 20
t = 1
Therefore, it will take 1 hour for Train B to catch up to Train A.
Since Train A passed the station at 11:15 a.m., Train B will catch up to Train A at 11:15 a.m. + 1 hour = 12:15 p.m.
So the answer is: 12:15 p.m.
Now, let's translate the expression "The product of 45% and some number" into algebraic expression:
Let the number be x.
The product of 45% (or 0.45) and some number x can be written as:
0.45 * x or simply 0.45x.