### 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.