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?

Result

s =  7.003 km

Solution:

v1=3.7 km/h v2=27 km/h t1=(x+42)/60 t2=(x56)/60 s=v1 t1=v2 t2 v1(x+42)=v2(x56) x=(v1 42+v2 56)/(v2v1)=(3.7 42+27 56)/(273.7)71.5622 min t1=(x+42)/60=(71.5622+42)/60=4412331.8927 h t2=(x56)/60=(71.562256)/600.2594 h  s=s1=s2 s1=v1 t1=3.7 1.89277.003 km s=v2 t2=27 0.25947.003=7.003  km v_{ 1 } = 3.7 \ km/h \ \\ v_{ 2 } = 27 \ 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 \ min \ \\ t_{ 1 } = (x + 42)/60 = (71.5622 + 42)/60 = \dfrac{ 441 }{ 233 } \doteq 1.8927 \ h \ \\ t_{ 2 } = (x - 56)/60 = (71.5622 - 56)/60 \doteq 0.2594 \ h \ \\ \ \\ s = s_{ 1 } = s_{ 2 } \ \\ s_{ 1 } = v_{ 1 } \cdot \ t_{ 1 } = 3.7 \cdot \ 1.8927 \doteq 7.003 \ km \ \\ s = v_{ 2 } \cdot \ t_{ 2 } = 27 \cdot \ 0.2594 \doteq 7.003 = 7.003 \ \text { km }







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

Showing 0 comments:
1st comment
Be the first to comment!
avatar




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?

Next similar math problems:

  1. The escalator
    eskalator I run up the escalator at a constant speed in the direction of the stairs and write down the number of steps A we climbed. Then we turn around and run it at the same constant speed in the opposite direction and write down the number of steps B that I climb
  2. The tourist
    tourist The tourist traveled 78km in 3 hours. Part of the journey went on foot at 6km/h, the rest of the trip by bus at 30km/h. How long did he walk?
  3. Three cats
    three_cats If three cats eat three mice in three minutes, after which time 260 cats eat 260 mice?
  4. Forestry workers
    forestry_workers In the forest is employed 56 laborers planting trees in nurseries. For 8 hour work day would end job in 37 days. After 16 days, 9 laborers go forth? How many days are needed to complete planting trees in nurseries by others, if they will work 10 hours a d
  5. AM of three numbers
    arithmet_seq The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers.
  6. Pool
    pool If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
  7. Geography tests
    test On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
  8. Year 2020
    eq222 The four-digit number divided by 2020 gives a result of 1, **. (Can not be in form 1,*0. ) Write all the options.
  9. Sum of the digits
    numbers2 How many are two-digit natural numbers that have the sum of the digits 9?
  10. 45th birthday
    clock-night-schr_1 This year Mrs. Clever celebrated her 45th birthday. Her three children are now 7.11 and 15 years old. In how many years will Mrs. Clever's age be equal to the sum of her children's years?
  11. Glasses
    okuliare There are 36 pupils in the class. Nine girls wear glasses. Boys with glasses are five less than girls without glasses. Boys without glasses are two times more than girls without glasses. How many boys and how many girls?
  12. Dividing money
    mince_2 Vilem, Cenek, and Edita divided the money they earned by spreading the leaflet. Vilem got 240 CZK more than Cenek and twice more than Edita. Edita got 400kc less than Vilem.
  13. Three glasses
    skleniceRGB Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the b
  14. Brick weight
    brick The brick weighs 2 kg and a half bricks. How much does one brick weigh?
  15. Trapezoid MO
    right_trapezium The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
  16. Garden
    garden_1 Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
  17. Bonus
    moeny Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses?