Question

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=300
B.) Square root (40t)^2+[60(t-2)]^2=300
C.) Square root (40t)^2+[60(t+2)]^2=300
D.) Square root (60t)^2+[40(t-2)]^2=300

Answer 1

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