A ship travels a distance of 700 km. On the return trip it averages 10km/hr faster and 8 hours less, tp travel the 700km back. Determine how long the original part of the trip took in hours

The total duration of the trip is 48 hours.

Step-by-step explanation:

Let suppose that ship travels at constant speed during its travel. Each stage is represented by the following kinematic equation:

Where:

- Travelled distance, measured in kilometers.

- Time, measured in hours.

- Speed, measured in kilometers per hour.

Now, each stage is represented by the following expressions:

Outbound trip

Return trip

By eliminating and simplifying the resulting expression algebraically:

This equation can be solved by means of the Quadratic Formula, whose roots are presented below:

and

Only the first roots offers a physically resonable solution. Then, total duration of the trip is:

The total duration of the trip is 48 hours.