# 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. **

**d _{AC}**

**+ d**

_{C}_{B}= d_{AB }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.

d_{AB} = 90 · 2 = 180 miles

d_{BC} = 60 · 2 = 120 miles

### Second ^{}Case Scenario

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

**d _{AC}**

**− d**

_{BC}= d_{AB }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:

d_{AB} = 90 · 6 = 540 miles.

d_{BC} = 60 · 6 = 360 miles.

### Third^{} Case Scenario

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

**d _{1} = d_{2 }**

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.

d_{1} = 90 · 12 = 1,080 miles