# Motion Word Problems

If a vehicle travels at a constant or uniform speed, the formula that relates distance, speed and time is:

Distance = speed × time

### First Case Scenario

The vehicles are travelling towards one another.

dAC + dCB = dAB

Two cities, A and B are located 300 miles from each other. At 9 am, a car leaves City A with a speed of 90 mph and travels towards City B. At the same time, a car leaves City B travelling towards City A with a speed of 60 mph. Find:

1 The time it takes for the cars to pass each other.

90t + 60t = 300     150t = 300      t = 2 hours

2 The time at which they passed each other.

They were at 11 of the morning.

3 The distance traveled by each at the time of them passing each other.

dAB = 90 · 2 = 180 miles

dBC = 60 · 2 = 120 miles

### Second Case Scenario

The vehicles are travelling in the same direction from different starting points.

dAC dBC = dAB

Two cities, A and B are located on the same east-west highway, 180 miles from each other. At 9 am, a car leaves each city, both travelling east. The car that leaves City A travels at 90 mph, and the car that leaves City B travels at 60 mph. Find:

1The time it takes for Car A to reach Car B:

90t − 60t = 180     30t = 180     t = 6 hours

2The time at which Car A reaches Car B:

Car A reaches Car B at 3 in the afternoon.

3 The distance traveled by each at the time of Car A reaching Car B:

dAB = 90 · 6 = 540 miles.

dBC = 60 · 6 = 360 miles.

### Third Case Scenario

The vehicles are travelling in the same direction with the same starting point.

d1 = d2

A car leaves a city with a speed of 90 mph. Three hours later and out of the same city another car in pursuit of the first leaves with a speed of 120 mph. Find:

1The time it takes for the second car to reach the first.

90t = 120 · (t − 3)

90t = 120t − 360      −30t = −360       t = 12 hours

2 The distance from the city when the second car reaches the first.

d1 = 90 · 12 = 1,080 miles