# Derivatives: Minimizing Time and Distance

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A lighthouse is 30 miles off a straight coast and a town is located 25 miles down the sea coast. Supplies are to be moved from the town to the lighthouse on a regular basis and at a minimum time. If the supplies can be moved at a rate of 4 miles per hour on water and 40 miles per hour on land, how far from the town should the dock be constructed for the shipment of supplies?

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#### Solution Preview

T - town, D - dock to be built, L - Lighthouse, C - coastal point perpendicular to lighthouse, x - distance between town and dock (unknown), 40mph on land, 4mph on ...

#### Solution Summary

Derivatives are used to calculate optimal distance.

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