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