Rate, Distance, Time - Problem, 6

Category: Algebra, Mechanics, Physics

"Published in Newark, California, USA"

The local train is 25 miles down the track from Central Station when the express leaves the station. The local train travels at a rate of 50 mi/hr and the express travels travels at a rate of 80 mi/hr. Let n represent the number of hours since the express train left Central Station.

(a) Write an expression that represents the express train's distance from Central Station in n hours.

(b) When will the express train catch up with the local train?

Solution:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life

Initially, the local train is already left from Central Station which is 25 miles apart. The time traveled by the local train is

 

 

   
If the express train leaves from Central Station which is faster than the local train, then the express train will catch up the local train at time n.

Photo by Math Principles in Everyday Life

(a) The distance traveled by the express train is
 

 

 

 

 
(b) Finally, the express train will catch up the local train at
 

 

 

 

 

 

 

 

or

Rate, Distance, Time - Problem, 4

Category: Algebra, Physics, Mechanics

"Published in Newark, California, USA"

Mr. Saldaña drove out to a place in the country at the rate of 40 miles per hour and came back the same way at the rate of 60 miles per hour. How far out did he drive if the entire trip took 7 hours?

Solution:

The given word problem is about the rate, distance, and time problem. Let's analyze the word problem as follows:

Let x = be the time of first travel at 40 miles per hour 
      y = be the time of return travel at 60 miles per hour

To understand more the word problem, it is better to illustrate the given word problem as follows 

 We know that

The first distance traveled by Mr. Sadaña is equal to his return distance because it is a round trip travel. The working equation for this statement will be equal to

The other working equation which is the total time traveled by Mr. Sadaña will be equal to

Substitute the value of x from the first equation to the above equation, we have

Hence, the return distance traveled by Mr. Sedaña will be equal to

Therefore, the total distance traveled by Mr. Sedaña is 

Word Problem - Race Problem

Category: Algebra, Physics, Mechanics

"Published in Newark, California, USA"

In a 100-meter race, Pepito gives Willie a 30-meter start and losses by 2 ½  seconds. In the second trial, he gives Willie a 10-meter start and beats him by 2 ½ seconds. Find the rate of each runner.

Solution:

The given word problem above is about a marathon or race problem. Let's analyze the word problem as follows:

Let x = be the rate of Willie
      y = be the rate of Pepito
       t = total time of Pepito to finish the 100-meter race

If the first statement says "In a 100-meter race, Pepito gives Willie a 30-meter start and losses by 2 ½  seconds.", then the working equation will be

 
Note:

If the second statement says "In the second trial, he gives Willie a 10-meter start and beats him by 2 ½ seconds.", then the working equation will be

Equate the first equation with the second equation because the two cases or trials are both in a 100-meter race

Substitute the value of x to either of the two equations above, we have

Hence, the value of y will be equal to

Therefore, the final answers are

Rate of Pepito = y = 5 meters per seconds
Rate of Willie =  x = 4 meters per seconds