Question

A ferry traveled 1 6 6 1 ​ start fraction, 1, divided by, 6, end fraction of the distance between two ports in 3 7 7 3 ​ start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate. At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?

Answer 1

`(7)/(18)` of the distance

Explanation:

We know that a ferry traveled
`(1)/(6)` of the distance between two ports in
`(3)/(7)` hours.

In order to calculate what fraction of the distance between the two ports can the ferry travel in one hour we can do the following reasoning :

The rate of the ferry is the same at any time.

The ferry will travel
`(1)/(6)` of the distance in
`(3)/(7)` hours.

If we divide each fraction by 3 ⇒

`((1)/(6))/(3)=(1)/(18)` and
`((3)/(7))/(3)=(1)/(7)`

We do this to obtain a ''1'' in the numerator of the second fraction (the hours fraction). Now, we can say that :

The ferry will travel
`(1)/(18)` of the distance in
`(1)/(7)` hours.

Finally, we multiply each fraction by 7 (in order to obtain the distance for 1 hour) ⇒

`((1)/(18)).7=(7)/(18)` and
`((1)/(7)).7=1`

We found out that the ferry will travel
`(7)/(18)` of the distance in 1 hour.