A family drove 1080 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2.5 hours longer. Determine their average speed on the way to the lodge.

Let the average speed to the lodge by x.

The time they took to go there is given by Time_{go} = \frac{1080}{x}

Now, their average speed is 6 less than the first. Hence, the new average speed is (x - 6) mil/hr.

The time is given by:

Time_{back} = \frac{1080}{x-6}

You are then told that this time is 2.5 hours longer than the first time... Hence:

Time_{back} - 2.5 = Time_{go}

\frac{1080}{x-6} - 2.5 = \frac{1080}{x}

Solve for x now.

Post what you get! :)