"Published in Newark, California, USA"
From Manila to a certain town in Batangas is some 224 miles. How long does it ordinarily take to reach the town, if by traveling 8 miles per hour faster, the trip is reduced by half an hour?
Solution:
The given word problem above is about rate, distance, and time problem with some conditions. Lets analyze the given word problem as follows:
Let x = be the rate in miles per hour
y = be the travel time in hour
We know that
The first working equation will be
If the statement says, "...if by traveling 8 miles per hour faster, the trip is reduced by half an hour?", then the second working equation will be
To eliminate y, substitute the value of y from the first working equation to the second equation, we have
Solve the quadratic equation by completing the square
Take the square root on both sides of the equation
In solving for the rate and time, we have to choose the positive value at the right side of the equation. Hence, the rate is
Therefore, the usual travel time is
