Speed Distance Problems
Speed = Distance/Time
OR Time = Distance/Speed
OR Distance = Speed * Time
1. Emilio drove from his home to Chicago at an average speed of 50mph. On the return trip he drove at an average speed of 55mph. The return trip took Emilio 1 hour less than the trip to Chicago. How many total hours did he travel?
Let time going to Chicago = x
Time coming from Chicago = x =1
Distance to Chicago = Distance returning from Chicago
Speed * time = Speed * time
50 (x) = 55 (x – 1)
50x = 55x – 55
5x = 55
x = 11
Total time = 11 + (11-1) = 21 hours
2. A car and a bus set out a 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car.
Let Speed of bus = x
Speed of car = 2x – 30
Distance Traveled by car in 2hours – distance traveled by bus in 2 hours = 20
2 (2x -30) + 2(x) = 20
4x – 60 + 2x = 20
2x – 60 = 20
2x = 80
x = 40; 2(40) – 30 =50 mph
Speed of car 50mph
3. A passenger train leave the train depot 2 hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours.
Let Speed of passenger train = x
Speed of freight train = x -20
In 3 + 2 hours freight train has traveled = 3(x-20) distance
In 3 hours the passenger train has traveled 3 x distances
3x = 5(x – 20)
3x = 5x –100
100 = 2x
x = 50
The passenger train is traveling at 50mph
Freight train is traveling at 30mph.
4. Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet?
Distance traveled by 1st cyclist + distance Traveled by second cyclist = 45
Note Distance = speed * time
14(x) + 16(x) = 45
30x = 45
x = 1.5
They will meet in 1.5 hours or 90 min.
5. A boat travels for three hours with a current of 3mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? How far did the boat travel one way?
Let speed of boat = x
Speed with current = x + 3
Speed against current = x – 3
Distance going = distance returning
3(x+3) = 4 (x -3)
3x + 9 = 4x -12
x = 21
3(2+3) = 3*24 = 72
Speed of boat = 21mph; It traveled 72 miles one way.
6. Two cars start from the same point and start travelling in opposite directions. One car is traveling at 65mph and the other is traveling at 72mph. After how many hours will the cars be 685 miles apart?
Let time = x
65(x) + 72(x) = 865
137x = 865
X = 5
The 2 cars will be 685 miles apart after 5 hours
7. Two cars start from the same point and start travelling in the same directions. One car is traveling at 65mph and the other is traveling at 56mph. After how many hours will the cars be 45 miles apart?
Let time = x
65(x) - 56(x) =45
9x = 45
X = 5
The 2 cars will be 45 miles apart after 5 hours.
8. An airplane starts from Airport A at a speed of 550mph going towards Airport B. Another airplane starts from Airport B at a speed of 600mph going towards Airport A. If the two airports are 4600 miles apart, after how many hours will they pass each other?
Let time = x
Distance travelled by 1st airplane = 550x
Distance travelled by second airplane = 600x
550x + 600x = 4500
1150x = 4600
X = 4
The two airplanes will pass one another after 4 hours.
9. An airplane starts from Airport A at a speed of 550mph going towards Airport B. Another airplane starts from Airport B at a speed of 650mph going towards Airport A. If the two airports are 4500 miles apart, after how many hours will still be 300 miles apart?
Let time = x
Distance travelled by 1st airplane = 550x
Distance travelled by second airplane = 650x
550x + 650x = 4500-300
1200x = 4200
x = 3.5
The two airplanes will pass one another after 3.5 hours.
10. Two cars start from the same town and drive in opposite directions. One car is 25mph faster than the other car. After driving for 4 hours they are 500 miles away from one another. Find the speed at which each car is driving?
Let speed of one car = x
Speed of other car = x+25
Distance traveled by 1st car in 4 hours = 4x
Distance traveled by 2nd car = 4(x+25)
4x + 4(x +25) = 500
4x + 4x + 100 = 500
8x + 100 = 500
8x = 400
X = 50
One car is traveling at 50mph, the other is traveling at 75mph.
11. Two cars start from the same town and drive in opposite directions. One car is 15 more than ½ the speed of the other car. After driving for 4 hours they are 510 miles away from one another. Find the speed at which each car is driving?
Let speed of one car = x
Speed of other car = ½ x+10
Distance traveled by 1st car in 4 hours = 4x
Distance traveled by 2nd car = 4( ½ x + 15)
4x + 4( ½ x +15) = 510
4x + 2x + 60 = 510
6x + 60 = 510
6x = 450
X = 75
One car is traveling at 75mph, the other is traveling at 52.5mph.
12. Jane starts driving from NY City to Rochester at 63mph. Two hours latter a train starts along the same route towards Rochester from NY City, If the train catches up with Lane’s car in 3 hours, how fast is the train traveling?
Let the speed of the train = x
Distance traveled by the train in 3 hours = 3x.
During this time the car has covered = 63(3+2) since the car started 2 hours ahead of the train.
63(2+3) = 3x
63(5) = 3x
315= 3x
105=x
The train is traveling at 105mph.
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