Distance,Speed and Time Problems
Question: Two bicycles start at the same point travelling in the opposite direction. The speed of second bike in miles per hour is 12 less than three times the first. At the end of 6 hours, the bicycles are 144 miles apart. Find the speed of each bicycle.
Solution:
Question: Two cars are driving in opposite directions, one at 55 mph and the other at 65 mph . How long will it take before the cars are 300 miles apart?
Solution:
Then the equation as follows
55x+65x=300
120x=300
x=2.5 hours
Check 55(2.5)+65(2.5)=300
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Question: At 8.00 AM a doctor leaves Sanford on a northbound train. Her husband, noticing that the doctor forgot her briefcase, boards another northbound train at 10.00 AM, and travelling 18 mph faster than the first train, the second train overtakes the first train at 4.00 PM . find the speeds of the trains, and the distance they traveled ?
Solution:
Let x be the speed of the first train.
Then as per the above question, let x+18 is the speed of second train.
The first train starts at 8 am and meets second train at 4 pm, It means it has taken 8 hrs to reach that point. similarly second train meets first train at 6 hrs.
Then the equation as follows:
8*x=6*(x+18)
8x=6x+108
2x=108
x=54.
Therefore the speed of first train is 54 mph.
Then the speed of second train is x+18=72 mph.
The distance traveled by both the trains is 8*x=8*54=432 miles
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Question: Two trains leave Winter park Terminal travelling in the opposite direction. The southbound train leaves at 8.00 am. The northbound train leaves at 10.00 am travelling 20 mph faster than the southbound train. At 2.00 pm the trains are 600 miles apart. find the speeds of the trains?
Solution:
Let x be the speed of the Southbound train.
Then as per the above question, let x+20 is the speed of Northbound train.
The first train starts at 8 am and meets second train at 2 pm, It means it has taken 6 hrs to reach that point. similarly second train meets first train at 4 hrs.
Then the equation as follows:
6*x+4*(x+20)=600
6x+4x+80=600
10x+80=600
10x=520
x=52 mph Southbound Train
x+20=52+20=72 mph Northbound Train.
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Question: Two bicycles begin at the same point on a circular path traveling in the same direction. The rate of one cyclist is 5 mph faster than the other. If it takes faster cyclist 3 hours to "lap" the slower cyclist, then determine the distance around the path. [Hint: The difference of the distance traveled equals one lap]. If the slower bicycle travels at 10 mph , how many laps did each bicycle make?
Solution:
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Question: Two bicyclist begin at same point on a circular path travelling in the same direction. One cyclist who is traveling 3 mph faster than the other, "laps" the cyclist after 6 laps. Find the speeds of cyclist . ?
Solution:
Solution:
Speed
|
*time
|
=Distance
|
|
1st Bicycle
|
x
|
6
|
6*x
|
2nd Bicycle
|
3x-12
|
6
|
6*(3x-12)
|
Total
|
144
|
Then the equation as follows
6*x+6*(3x-12)=144
6x+18x-72=144
24x=216
x=9 miles per hour for 1st bicycle.
3x-12=27-12=15 miles per hour for 2nd Bicycle.
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Question: A Train leaves the Secunderabad station averaging 45mph. A second train leaves the same station two hours later after averaging 60 mph. How long will it take the second train to catch the first train?
Solution:
Speed
|
*time
|
=Distance
|
|
1st Train
|
45
|
x+2
|
45*(x+2)
|
2nd Train
|
60
|
x
|
60*x
|
Then the equation as follows
45*(x+2)=60x
45x+90=60x
15x=90
x=6
Therefore it takes second train to catch first train at 6 hours.
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Question: Two boys are riding bicycles in the opposite direction.One travels 15mph faster than the other. At the end of 3 hours they are 102 miles apart. How much fast is each boy is riding?
Solution:
Then the equation as follows
3*(x+15)+3x=102
3x+45+3x=102
6x+45=102
6x=57
x=9.5mph 2nd bicycle
x+15 =9.5+15=24.5 mph 1st bicycle.
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Question: Two boys are riding bicycles in the opposite direction.One travels 15mph faster than the other. At the end of 3 hours they are 102 miles apart. How much fast is each boy is riding?
Solution:
Speed
|
*time
|
=Distance
|
|
1st Bicycle
|
x+15
|
3
|
3*(x+15)
|
2nd Bicycle
|
x
|
3
|
3*x
|
Total
|
102
|
Then the equation as follows
3*(x+15)+3x=102
3x+45+3x=102
6x+45=102
6x=57
x=9.5mph 2nd bicycle
x+15 =9.5+15=24.5 mph 1st bicycle.
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Question: Two cars are driving in opposite directions, one at 55 mph and the other at 65 mph . How long will it take before the cars are 300 miles apart?
Solution:
Speed
|
*time
|
=Distance
|
|
1st car
|
55
|
x
|
x*55
|
2nd car
|
65
|
x
|
x*65
|
Total
|
300
|
Then the equation as follows
55x+65x=300
120x=300
x=2.5 hours
Check 55(2.5)+65(2.5)=300
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Question: At 8.00 AM a doctor leaves Sanford on a northbound train. Her husband, noticing that the doctor forgot her briefcase, boards another northbound train at 10.00 AM, and travelling 18 mph faster than the first train, the second train overtakes the first train at 4.00 PM . find the speeds of the trains, and the distance they traveled ?
Solution:
Speed
|
*time
|
=Distance
|
|
1st train
|
x
|
8
|
8*x
|
2nd train
|
x+18
|
6
|
6*(x+18)
|
Let x be the speed of the first train.
Then as per the above question, let x+18 is the speed of second train.
The first train starts at 8 am and meets second train at 4 pm, It means it has taken 8 hrs to reach that point. similarly second train meets first train at 6 hrs.
Then the equation as follows:
8*x=6*(x+18)
8x=6x+108
2x=108
x=54.
Therefore the speed of first train is 54 mph.
Then the speed of second train is x+18=72 mph.
The distance traveled by both the trains is 8*x=8*54=432 miles
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Question: Two trains leave Winter park Terminal travelling in the opposite direction. The southbound train leaves at 8.00 am. The northbound train leaves at 10.00 am travelling 20 mph faster than the southbound train. At 2.00 pm the trains are 600 miles apart. find the speeds of the trains?
Solution:
Speed
|
*time
|
=Distance
|
|
Southbound Train
|
x
|
6
|
6*x
|
Northbound Train
|
x+20
|
4
|
4*(x+20)
|
Total
|
600
|
Let x be the speed of the Southbound train.
Then as per the above question, let x+20 is the speed of Northbound train.
The first train starts at 8 am and meets second train at 2 pm, It means it has taken 6 hrs to reach that point. similarly second train meets first train at 4 hrs.
Then the equation as follows:
6*x+4*(x+20)=600
6x+4x+80=600
10x+80=600
10x=520
x=52 mph Southbound Train
x+20=52+20=72 mph Northbound Train.
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Question: Two bicycles begin at the same point on a circular path traveling in the same direction. The rate of one cyclist is 5 mph faster than the other. If it takes faster cyclist 3 hours to "lap" the slower cyclist, then determine the distance around the path. [Hint: The difference of the distance traveled equals one lap]. If the slower bicycle travels at 10 mph , how many laps did each bicycle make?
Solution:
Two bicycles begin at the same point on a circular path traveling in the same direction.
The rate of one cyclist is 5 mph faster than the other.
If it takes faster cyclist 3 hours to "lap" the slower cyclist, then determine the distance around the path.
:
The relative speed between the cyclists is 5 mph, and it takes 3 hrs to lap:
3 * 5 = 15 mi is the distance around the circular path
:
If the slower bicycle travels at 10 mph, how many laps did each bicycle make?
:
In 3 hrs the slower bike would travel: 3*10 = 30 mi; 30/15 = 2 laps
In 3 hrs the faster bike would travel: 3*15 = 45 mi; 45/15 = 3 laps
The rate of one cyclist is 5 mph faster than the other.
If it takes faster cyclist 3 hours to "lap" the slower cyclist, then determine the distance around the path.
:
The relative speed between the cyclists is 5 mph, and it takes 3 hrs to lap:
3 * 5 = 15 mi is the distance around the circular path
:
If the slower bicycle travels at 10 mph, how many laps did each bicycle make?
:
In 3 hrs the slower bike would travel: 3*10 = 30 mi; 30/15 = 2 laps
In 3 hrs the faster bike would travel: 3*15 = 45 mi; 45/15 = 3 laps
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Question: Two bicyclist begin at same point on a circular path travelling in the same direction. One cyclist who is traveling 3 mph faster than the other, "laps" the cyclist after 6 laps. Find the speeds of cyclist . ?
Solution:
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