Classic Rate, Time, Distance ProblemDate: 09/30/2004 at 00:43:03 From: Cindy Subject: rate, time and distance If Joe travels at 50 mph, he arrives at a certain destination 20 minutes faster than if he travels at 45 mph. How far does he travel? I know that rate times time equals distance. I even know that the answer is 150 miles, but I cannot figure out how to write an equation to make it work. Please help!!! Date: 09/30/2004 at 07:27:53 From: Doctor Wilko Subject: Re: rate, time and distance Hi Cindy, Thanks for writing to Dr. Math! I found a nice way to approach these kinds of problems. First, I try to draw a picture of what is going on, and then I try to organize the data in a way that makes it easier to understand. As you suggested, we are going to be using the equation: Distance = Rate * Time D = R * T Since you are given the rate in 'miles per hour' (mph), then your time should be in 'hours' so that the units are all the same. One key to solving this problem is to note that 20 minutes is the same as 20/60 of an hour which reduces to 1/3 of an hour. First, draw a picture: Joe drives at 45 mph: ---------------> [drives this distance in x hours] Joe drives at 50 mph: ---------------> [drives the same distance in (x - 1/3) hours] The pictures help me organize my thoughts and visualize the situation better. Now let's organize the data: - You know two rates at which Joe can drive the unknown distance: 45 mph and 50 mph. - You don't know what time it takes to drive the distance at 45 mph, but you DO know that it takes 1/3 hour less to drive the same distance at 50 mph. Let's call x the time in hours it takes to drive the unknown distance at 45 mph. From this, if it takes x hours to drive the unknown distance at 45 mph, you can conclude that it takes (x - 1/3) hours to drive the distance at 50 mph. - You want to know the distance in miles that Joe travels. I'll put this into an organized format below. I get distance from the formula that D = R*T. --------------------------------------------------------------- | | Time Rate Distance | ---------------------------------------------------------------| | 45 mph | x hours 45 mph 45x miles | |----------|----------------------------------------------------| | 50 mph | (x - 1/3) hours 50 mph 50(x - 1/3) miles | --------------------------------------------------------------- To find x, note that Joe is only driving one distance, but varying his speed (rate) each time, so you know the distances above are equal. If you set them equal you can find x, which is the time in hours to drive the unknown distance at 45 mph. Once you get x, plug it back into either of the distances above to get the total distance in miles that Joe travels. Does this help? Please write back if you need anything else. - Doctor Wilko, The Math Forum http://mathforum.org/dr.math/ |
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