Question

A cruise ship is traveling at a rate of 20 miles per hour. How do you use a direct formula to calculate the number of miles travelled in 7 hours?

Answer 1

Hint: In this problem, we are given that a cruise ship is traveling at a rate of 20 miles per hour and we have to find the number of miles travelled in 7 hours. Here we can see that the given data is based on direct comparison between two different quantities. We can also see that the given problem is an example of direct proportion and we have to use a direct variation formula, as if the number of hours increases, the miles travelled also increases. We can write it in mathematical form to get the answer.

Complete step-by-step solution:
We know that the direct variation formula is,
\[y=kx\]
Where in this problem,
\[\Rightarrow y\left( miles \right)=20miles/hour\times x\left( hours \right)\]
We are given that a cruise ship is traveling at a rate of 20 miles per hour, we can write it as
\[\Rightarrow y=20x\]
We have to find the number of miles travelled in 7 hours, we can substitute x = 7.
We know that the variable y is the unknown miles.
We can now write it as,
\[\Rightarrow y=20\left( 7 \right)=140\]
We know that the given problem is an example of direct as if the number of hours increases, the miles travelled also increases.
Therefore, the ship can travel 140 miles in 7 hours.

Note: Students make mistakes while comparing the given data, as the given data is based on direct comparison between two different quantities. We should also remember that direct proportion is nothing but, if a quantity of one object increases, then the quantity of its relating result also increases.