# Motion

If you go at speed 3.7 km/h, you come to the station 42 minutes after leaving the train. If you go by bike to the station at speed 27 km/h, you come to the station 56 minutes before its departure.
How far is the train station?

Correct result:

s =  7.003 km

#### Solution:

$v_{1}=3.7 \ \text{km/h} \ \\ v_{2}=27 \ \text{km/h} \ \\ t_{1}=(x + 42)/60 \ \\ t_{2}=(x - 56)/60 \ \\ s=v_{1} \cdot \ t_{1}=v_{2} \cdot \ t_{2} \ \\ v_{1}( x+ 42 )=v_{2}( x - 56 ) \ \\ x=(v_{1} \cdot \ 42+v_{2} \cdot \ 56)/(v_{2}-v_{1})=(3.7 \cdot \ 42+27 \cdot \ 56)/(27-3.7) \doteq 71.5622 \ \text{min} \ \\ t_{1}=(x + 42)/60=(71.5622 + 42)/60 \doteq \dfrac{ 441 }{ 233 } \doteq 1.8927 \ \text{h} \ \\ t_{2}=(x - 56)/60=(71.5622 - 56)/60 \doteq 0.2594 \ \text{h} \ \\ \ \\ s=s_{1}=s_{2} \ \\ s_{1}=v_{1} \cdot \ t_{1}=3.7 \cdot \ 1.8927 \doteq 7.003 \ \text{km} \ \\ s=v_{2} \cdot \ t_{2}=27 \cdot \ 0.2594=7.003 \ \text{km}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Check out our ratio calculator.
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
Do you want to convert length units?
Do you want to convert velocity (speed) units?
Do you want to convert time units like minutes to seconds?

## Next similar math problems:

• The tower
The observer sees the base of the tower 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands?
• Water mixing
We have 520 ml of hot water and 640 ml of water at 48°C. What is the temperature of approximately hot water when the resulting mixture has a temperature of 65°C?
• In the
In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
• Lookout tower
How high is the lookout tower? If each step was 3 cm lower, there would be 60 more of them on the lookout tower. If it was 3 cm higher again, it would be 40 less than it is now.
• Coordinates
Determine the coordinates of the vertices and the content of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0
• A bottle
A bottle full of cola weighs 1,320 g. If we drink three-tenths of it, it will weigh 1,008g. How much does an empty bottle weigh?
• Summands
We want to split the number 110 into three summands so that the first and the second summand are in the ratio 4: 5, and the third with the first are in ratio 7: 3. Calculate the smallest of the summands.
• Columns of two and three
When students in one class stand in columns of two there is none left. When he stands in columns of three, there is one student left. There are 5 more double columns than three columns. How many students are in the class?
• The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
• Side lengths
In the triangle ABC, the height to the side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b.