# James drove 200 miles in 4 hours at this rate what is the total number of hours it will take him to drive 150 miles

where D stands for distance, R stands for the rate or speed, and T stands for the time. You use this equation lots of times. Think, "If I go at 50 miles per hour (rate) and I drive for 3 hours (time), how far do I travel?" You do this in your head ... 50 miles every hour then in 3 hours you go 150 miles. . In this problem we are going to be using this equation to calculate the rate. Think, "If I go 150 miles and I drive for 3 hours, how many miles per hour did I go?" This time you can see that to go 150 miles in 3 hours you have to average 50 miles per hour as your rate. That's pretty basically what we are going to be doing. . Now back to the problem. The first part of the problem tells you that you drive at 50 mph for 4 hours. How far did you go? . Use the equation: . and substitute 50 for R and 4 for T to get: . miles. . So the distance you want to travel is 200 miles. . Now the problem asks you how fast you have to go (rate) if you want to cover the same distance in 2.5 hours. . Return to the equation: . and substitute 200 miles for D and 2.5 hours for T to get: . . You can find R by dividing both sides by 2.5 and when you do you get: . . This simplifies to: . . You can divide 2.5 into 200 and find that the answer is 80. So the final answer is that to go 200 miles in 2.5 hours you have to travel at a rate of 80 miles per hour. . Too fast for safety and wastes gas. . Hope this discussion helps you to understand the problem a little more.