Practice Problem #1
By: Oliver Shi
Daquan, who lives in Dallas, wants to go to Houston for a cruise. There are 2 ways to drive from Dallas to Houston. Daquan could take the long route which is to take Road A and then make a 90 degree turn to Road B, or he could take a shortcut by taking Road C. Daquan wants to know how much faster it would be than taking Road A then Road B if he traveled at a constant speed of 50 mile per hour.
First, find the length of Road C. Since Road A, B, & C form a right triangle, Road C is equal to the sqrt(Road A^2 + Road B^2) = sqrt(400^2 + 300^2) = sqrt(1600 + 900) = sqrt(2500) = 500mi. Second, find distance it takes to travel to Houston using Road A & B. To get this you add together the lengths of these roads which equals 700 miles. Subsequently, find the time needed to travel this distance which is 700/50 = 14 hours. Then, find the time it take to travel to Houston using Road C which is 500/50 = 10 hours. Finally subtract the time needed to travel using Road A & B from the time needed to travel using Road C which gives you 4 hours. 4 hours is how much faster it is to use Road C rather than Road A & B.