Question

On the number line, a bug P is moving in the positive direction from the point 0, and a bug N is moving in the negative direction from the point 0. The speeds of both bugs are constant. Both leave 0 at the same time, and four seconds later P has reached 12 and N has reached –8.If x is the point reached by P after t seconds, and y is the point reached by N after t seconds, express x and y in terms of t.30 seconds after leaving point 0, how far apart are P and N?When will P and N be 300 units apart?

Answer 1

Answer:

x = 3t and y = 2t

The distance between P and N after 30 seconds is 150 units

P and N will be 300 units apart after 60 seconds

Step-by-step explanation:

∵ The bugs moved with constant speeds

∵ Speed = Distance ÷ Time

∵ Bug P moved 12 units in 4 sec.

∴ Its speed = 12 ÷ 4 = 3 units/sec.

∵ Bug N moved 8 units in 4 sec.

∴ Its speed = 8 ÷ 4 = 2 units/sec.

∵ P reached point x after t seconds

∴ x = 3t

∵ N reached point y after t seconds

∴ y = 2t

∵ t = 30 sec.

∴ x = 3 × 30 = 90 units

∴ y = 2 × 30 = 60 units

∴ The distance between x and y = 90 + 60 = 150 units

∵ The distance between x and y = 300 units

∴ 3t + 2t = 300

∴ 5t = 300

∴ t = 300 ÷ 5 = 60 sec.