Question

1.Two robots start out at 426c cm. apart and drive towards each other. The first robot drives at 5 cm per second and the second robot drives at 7 cm. per second. How long will it take until the robots meet?
In your response below, please answer each of the following questions:
a. What is the question being asked?
b. What are the important numbers?
c. Are their any variables?
d. Write an equation.
e. Solve the equation.
f. Do you think your answer is reasonable? Explain.

Answer 1

Answer:

a. The time it will take for the two robots meet

b. The important numbers are;

426 (cm), 5 (cm/second) and 7 (cm/second)

c. Yes, there are variables

d. The equation is 5 cm/s × t + 7 cm/s × t = 426 cm

e. The solution of the equation is, t = 35.5 seconds

f. Yes, the answer is reasonable

Explanation:

a. The question being asked is the time duration that will elapse before the two robots meet

b. The important numbers are;

The distance apart from which the two robots start out, d = 426 cm

The  speed of the first robot, v₁ = 5 cm/second

The  speed of the second robot, v₂ = 7 cm/second

c. The variables are;

The distance apart of the two robots = d

The  speed of the first robot = v₁

The  speed of the second robot = v₂

The time it takes for the two robots to meet = t

d. The equation is;

v₁ × t + v₂ × t = d

Plugging in the known values of v₁, v₂, we have;

5 cm/s × t + 7 cm/s × t = 426 cm...(1)

e. Solving the equation (1) above gives;

5 cm/s × t + 7 cm/s × t = t × (5 cm/s + 7 cm/s) = t × 12 cm/s = 426 cm

∴ t = 426 cm/(12 cm/s) = 35.5 s

t = 35.5 seconds

f. The time it would take the two robots to meet, t = 35.5 seconds

The answer is reasonable, given that the distance moved by each robot in the given time are;

The distance moved by the first robot, d₁ = 35.5 s × 5 cm/s = 177.5 cm

The distance moved by the second robot, d₂ = 35.5 s × 7 cm/s = 248.5 cm

d₁ + d₂ = 177.5 cm + 248.5 cm = 426 cm.