which of the following equations can be used to calculate the values of t for which the distance between Chris and any is 300 miles

The first thing we must know in this case is that the distance is equal to the speed for time.
We have then:
For Chris:
d1 = 40 * t
For Amy:
d2 = 60 * (t-2)
The distance between both will be given by the hypotenuse of the rectangle triangle:
300 = root ((40 * t) ^ 2 + (60 * (t-2)) ^ 2)
Answer:
300 = root ((40 * t) ^ 2 + (60 * (t-2)) ^ 2)
option 3

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Professor1994 Professor1994 · Answer 2 · 2018-03-14T18:21:43+01:00

Time that Chris has been driving: t
Velocity of Chris: V1=40 mph
Distance traveled by Chris: d1 (The horizontal side of the right triangle in the figure)

We have:
V=d/t

Applying this formula for the case of Chris:
V1=d1/t
Replacing the known values:
40 mph = d1/t
Solving for d1:
t (40) = t (d1/t)
40t = d1
d1 = 40t

Amy leaves two hours later, then the time for Amy is the time for Chirs minus 2 hours:
Time for Amy: t2=t-2
Velocity of Amy: V2=60 mph
Distance traveled by Amy: d2 (The vertical side of the right triangle in the figure)

Applying the formula of Velocity for Amy:
V2=d2 / t2
Replacing the known values:
60 mph = d2 / (t-2)
Solving for d2:
(t-2) (60) = (t-2) [ d2 / (t-2) ]
60(t-2) = d2
d2=60(t-2)

The Distance D between Chris and Amy is the hypothenuse of the right triangle, then we can use the Pythagorean Theorem to calculate it:
c^2=a^2+b^2, where c is the hypohenuse and a and b are the legs, the sides that form the right angle (the angle of 90°)

According with the figure:
c=D=300 miles
a=d1=40t
b=d2=60(t-2)

Replacing in the Pythagoras Theorem:
300^2 = (40t)^2 + [ 60(t-2) ]^2
Square root both sides of the equation:
sqrt(300^2) = sqrt { (40)^2 + [ 60(t-2) ]^2 }
300 = sqrt { (40t)^2 + [ 60(t-2) ] ^2 }
sqrt { (40t)^2 + [ 60(t-2) ]^2 } = 300

Answer: Third option