Video: Calculate a Percent Increase of Speed to Find the Difference in Time When the Distance Is Constant

Samantha lives in Missouri. She went to visit her aunt in Chicago. She took a taxi from her home to the train station and then took the train to Chicago and finally took a bus to her aunt’s home. The given table shows the distance, in miles, and the average speed, in miles per hour, for each part of the journey. For the journey summarized in the table, Samantha discovers that she could have taken a train with an average speed which is 16% faster than the one she took. If Samantha had taken the faster train instead, how much time would she have saved on her journey, in minutes? Assume that both trains depart at the same time and that there are no additional delays on Samantha’s journey.

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Video Transcript

Samantha lives in Missouri. She went to visit her aunt in Chicago. She took a taxi from her home to the train station and then took the train to Chicago and finally took a bus to her aunt’s home. The given table shows the distance, in miles, and the average speed, in miles per hour, for each part of the journey. For the journey summarized in the table, Samantha discovers that she could have taken a train with an average speed which is 16 percent faster than the one she took. If Samantha had taken the faster train instead, how much time would she have saved on her journey, in minutes? Assume that both trains depart at the same time and that there are no additional delays on Samantha’s journey.

First, we need to remember that the time something takes is equal to the distance divided by the speed. First, we’ll consider the train that Samantha actually took. We’ll need to know its speed, the distance travelled, and the time travelled for this train. And then, we’ll need to know the speed, the distance, and the time travelled for the faster train. We can find the speed of the first train by looking in the table. The average speed in miles per hour for the first train is 150 miles per hour. And the distance travelled on the first train is found in the table under the distance column. Samantha travelled 870 miles on the first train. And we remember that the time that Samantha was on the first train will be equal to the distance divided by speed. 870 miles divided by 150 miles per hour equals 5.8 hours.

Now, we need to consider these details for the faster train. The faster train is travelling 16 percent faster than 150 miles per hour. The faster train would still have to travel the same distance, 870 miles. But in order to calculate the time of the faster train, we need an exact answer for the speed of the faster train. And that means we need to know how to calculate 16 percent faster than 150 miles per hour. 16 percent faster means we’re dealing with a 16 percent increase than 150 miles per hour. We would then need to multiply our speed, 150 miles per hour, by 1.16. 0.16 represents an increase of 16 percent. 16 percent, written as a decimal, is 0.16. And we have the whole number one because the faster train is travelling the speed of the first train plus 16 percent. So we have one whole plus 16 percent.

We can move that up to our speed line. 150 times 1.16 equals 174, which is a measure of speed in miles per hour. The faster train was travelling 174 miles per hour. This means we’re ready to consider how long the second train was travelling. That will be its distance divided by its speed. 870 miles divided by 174 miles per hour equals five hours. The first train travelled for 5.8 hours, and the second train only travelled for five hours. This is a difference of 0.8 hours.

But we’re not looking for how much faster in hours. We’re looking for how much faster in minutes. And so, we need to convert 0.8 hours into minutes. Since we know that there are 60 minutes in every hour, we can multiply 0.8 hours by 60 minutes. 0.8 times 60 equals 48. And this tells us that the faster train was 48 minutes faster.

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