Chris and Amy leave from work and drive in different directions. Their paths are at a 90-degree angle from one another, as shown in the following illustration.Chris is traveling at 40 mph. Amy leaves two hours later and is traveling at 60 mph. Assuming that t represents the time that Chris has been driving, which of the following equations can be used to calculate the values of t for which the distance between Chris and Amy is 300 miles?A.) Square root (40t)^2-[60(t-2)]^2=300B.) Square root (40t)^2+[60(t-2)]^2=300C.) Square root (40t)^2+[60(t+2)]^2=300D.) Square root (60t)^2+[40(t-2)]^2=300
Accepted Solution
A:
we know that
the drawing is not necessary to solve the problem
t-----------> represents the time that Chris has been driving so Chris distance is y=40*t
Amy distance is y=60*(t-2)
applying the Pythagorean theorem let a----------> Chris distance b----------> Amy distance c----------> distance between Chris and Amy-------> 300 miles
c²=a²+b² so 300²=[40*t]²+[60*(t-2)]²--------> 300=√{[40*t]²+[60*(t-2)]}
the answer is the option B.) Square root (40t)^2+[60(t-2)]^2=300