Solve the problem.
-Two vehicles leave the same corner at the same time and travel at a right angle to each other. One vehicle travels 4 kilometers an hour faster than the other. If after one hour the vehicles are 20 kilometers apart, find the
Rate of each vehicle.
A) Slower vehicle: 8 km/hr; faster vehicle: 12 km/hr
B) Slower vehicle: -16 km/hr; faster vehicle: -12 km/hr
C) Slower vehicle: 12 km/hr; faster vehicle: 16 km/hr
D) Slower vehicle: 16 km/hr; faster vehicle: 20 km/hr

Question

Quizplus · Accepted Answer

Let x be the rate of the slower vehicle.

Then the rate of the faster vehicle is x + 4.

Since the vehicles travel at a right angle to each other, their distance after one hour can be found using the Pythagorean theorem:

distance² = (rate of slower vehicle)² + (rate of faster vehicle)²

Substituting the given values:

20² = x² + (x + 4)²

400 = x² + x² + 8x + 16

2x² + 8x - 384 = 0

x² + 4x - 192 = 0

(x - 12)(x + 16) = 0

x = 12 (since the rate cannot be negative)

Therefore, the rate of the slower vehicle is 12 km/hr and the rate of the faster vehicle is 16 km/hr.

So, the answer is C. Let x be the speed of the slower vehicle in km/hr. Then the speed of the faster vehicle is x+4 km/hr.

After one hour, the slower vehicle has travelled x km and the faster vehicle has travelled x+4 km. The distance between them is the hypotenuse of a right triangle with legs x km and x+4 km. By the Pythagorean Theorem:

distance^2 = x^2 + (x+4)^2

Simplifying this equation gives:

distance^2 = 2x^2 + 8x + 16

distance^2 - 16 = 2(x+2)^2

(x+2)^2 = (distance^2 - 16)/2

Taking the square root of both sides gives:

x+2 = sqrt((distance^2 - 16)/2)

x = sqrt((distance^2 - 16)/2) - 2

Plugging in the given distance of 20 km and simplifying gives:

x = 6 km/hr

Therefore, the speed of the slower vehicle is 6 km/hr and the speed of the faster vehicle is 10 km/hr (6+4). The correct choice is C.

Solve the Problem. -Two Vehicles Leave the Same Corner at the Same Time