Write rates comparing the number of traveled miles to the time in both situations. Use them to form a proportion.
120 miles
Practice makes perfect
We are told that a train travels 10 miles every 14 hour. Knowing that, we want to determine how far it travels in 3 hours. Let's start with arranging the given data in a table. Our table will have one row for the traveled distance and one row for the time. We can mark the missing distance as x.
Distance (mi)
10
x
Time (h)
14
3
For both of these situations we can write rates comparing the number of traveled miles to the time. To do so, we will write fractions with distance in the numerator and time in the denominator.
240miles in 14hour:& 10/14 [1.7ex]
xmiles in 3hours:& x/3
At the beginning we were told that the train travels 10 miles every 14 hour. This means that all the rates comparing the train's distance to the time are equivalent. So, the distance is proportional to time. Because of that both of our rates are equal and we can write a proportion.
10/14=x/3
We will solve the proportion to find the value of x. We can use the Cross Products Property. Let's do it!
