How to apply quadratic equations

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The sum of a number and its reciprocal is $\frac{13}{6}$ $\frac{13}{6}$ . Find the number.
A basketball court measuring 29 m by 15 m has an equal-width pathway all around it, with a total area of 792 m $^2$ $^{2}$ . Find the width of the pathway.
The height of a right-angled triangle is 24 cm less than 4 times its base length. If the area is 14 cm $^2$ $^{2}$ , find the lengths of the base and height.
Desmond is driving to Seattle which is 175km away from home. He left home an hour later than he planned to. If he wants to reach the destination in time, he has to increase his speed by 20km/hr from his usual speed. Determine his usual speed.
A boat can travel with a speed of 6 km/hr in still water. It takes the boat 2 hours longer to travel 16 km upstream than to make the return trip downstream. Find the speed of the current.

Applications of quadratic equations