Example of distance - rate problems, Algebra

Two cars are 500 miles apart & directly moving towards each other.  One car is at a speed of 100 mph and the other is at 70 mph.  Supposing that the cars start at the same time how much time it take for the two cars to meet?

Solution

Let's assume t represent the amount of time which the cars are traveling before they meet.  Now, we have to sketch a figure for this one. This figure will help us to write the equation which we'll have to solve out.

1270_Example of Distance - rate problems.png

From this figure we can note that the Distance Car A travels as well as the Distance Car B travels has to equal the total distance separating the two cars, 500 miles.

Following is the word equation for this problem into two separate forms.

1466_Example of Distance - rate problems1.png

We utilized the standard formula here twice, once for each car. We know that the distance a car travels is the rate of the car times the time traveled by the car.  In this case we know that Car A travels at 100 mph for t hours & that Car B travel at 70 mph for t hours as well. Plugging these in the word equation and solving out gives us,

100t + 70t = 500

170t = 500

t = 500/170  =2.941176 hrs

Thus, they will travel for approximately 2.94 hours before meeting.

Posted Date: 4/6/2013 3:46:19 AM | Location : United States







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