# Speed Problem Solving

by Mikayla (Oklahoma, United States) A truck left a depot at noon traveling an average speed of 40 kilometers per hour.How far from the depot and what time will it overtake another truck, which left the same depot 2 hours earlier and was traveling 30 kilometers per hour.Remember the formula: When identifying the parts of the word problem, distance is typically given in units of miles, meters, kilometers, or inches.

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Let t be the time it takes the truck traveling 40 km/h to overtake the truck traveling 30 km/h.

Then, the truck traveling 30 km/h will be overtaken in t 2 hours Truck traveling 40 km/hd = vtd = 40t Truck traveling 30 km/hd = vtd = 30(t 2)Truck traveling 40 km/h will meet with truck traveling 30 km/h when the distance is the same.40t = 30(t 2)40t = 30t 6040t - 30t = 30t - 30t 6010t = 60Since 10 times 6 = 60, then t = 6Truck traveling 40 km/h will overtake the other truck after 6 hours or at pmd = 40 x 6 = 240d = 30 x(6 2)d = 30 x 8 = 240The trucks will be 240 km away from the depot.

For example, if you know the time and rate a person is traveling on a train, you can quickly calculate how far he traveled.

And if you know the time and distance a passenger traveled on a plane, you could quickly figure the distance she traveled simply by reconfiguring the formula.

Finally, use some common sense and decide if the answer found in step 6 makes sense.

For example, if you are trying to find the speed of a bicycle and your answer is –16 miles per hour or 95 miles per hour, these answers are probably wrong because it does not make sense that a bicycle can travel –16 or 95 miles per hour.Second, it is convenient to convert miles per half hour to miles per hour.35 miles per half hour is 70 miles per hour.Lastly, convert the formula from speed to distance. How far is a house in Florida if it takes you 4 hours to get there and your instantaneous speeds were 70 miles per hour, 50 miles per hour, 60 miles per hour, 10 miles per hour, and 0 miles per hour?Distance is the length of space traveled by a moving object or the length measured between two points. Time is the measured or measurable period during which an action, process, or condition exists or continues.In distance, rate, and time problems, time is measured as the fraction in which a particular distance is traveled.If the answer does not make sense, try doing the problem again.Example 1 – The Lazy River has a current of 2 miles per hour.Create a Distance, Rate, and Time chart similar to the one shown below.I always create a 3 by 3 chart and label the left side based on the problem at hand, the last row is always labeled “Total”.You may wish to draw a diagram to show what is happening.Organize the information you have in a chart format if you haven't solved these types of problems before.

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