Sueraiuka
contestada

*Two buses were coming from two different places situated just in the opposite
direction. The average speed of one bus is 5 km/hr more than that of another on
and they had started their journey in the same time. If the distance between
places is 500 km and they meet after 4 hours, find their speed.​

Respuesta :

tramserran

Answer:  60 km/hr and 65 km/hr

Step-by-step explanation:

        o-----------------------------------←500→-------------------------------------o

        Bus 1: rate = r + 5                                              Bus 2: rate = r            

                  time = 4                                                               time = 4

                  distance = d                                                        distance = 500 - d

                              Use distance = rate x time

      Bus 1: d = 4(r + 5)                                               Bus 2: 500 - d = 4(r)

                d = 4r + 20                                                    -d = 4r - 500

                                                                                      d = 500 - 4r

Solve the System of Equations using the Substitution method:

                                    4r + 20 = 500 - 4r

                                    8r + 20 = 500

                                   8r          = 480

                                              r = 60

    Bus 1: rate = r + 5                                              Bus 2: rate = r

                     = 60 + 5                                                              = 60

                     = 65

                 

BrainlyWarrior

Answer :

Distance between both buses = 500km

Time taken by them to meet each other = 4hr

Let speed of bus A be v km/hr.

ATQ, speed of bus B is 5km/ hr more than that of bus A.

∴ Speed of bus B will be (v + 5) km/hr.

★ Diagram :

[tex]\boxed{\setlength{\unitlength}{1cm}\begin{picture}(6,2)\thicklines\put(1,1){\circle*{0.2}}\put(5,1){\circle*{0.2}}\put(1,1){\vector(1,0){1}}\put(5,1){\vector(-1,0){1.5}}\put(0.2,0.9){A}\put(5.5,0.9){B}\put(1.4,1.2){v}\put(3.85,1.2){v+5}\put(2.35,0.4){\sf{500\;km}}\put(2.2,0.5){\vector(-1,0){1.3}}\put(3.55,0.5){\vector(1,0){1.5}}\end{picture}}[/tex]

★ As we know that,

  • Speed = Distance/Time ... (I)

Assuming both buses as point masses,

Relative speed of object A wrt object B when the object B moves in the opposite direction of A is given by

  • [tex]\boxed{\bf{v_{AB}=v_A+v_B}}[/tex]

Relative speed of bus A wrt B :

[tex]:\implies\:\sf{v_{AB}=v_A+v_B}[/tex]

[tex]:\implies\sf\:v_{AB}=v+(v+5)[/tex]

[tex]:\implies\bf\:v_{AB}=2v+5[/tex]

By substituting values in (I), we get

[tex]\leadsto\sf\:v_{AB}=\dfrac{d}{t}[/tex]

[tex]\leadsto\sf\:2v+5=\dfrac{500}{4}[/tex]

[tex]\leadsto\sf\:2v+5=125[/tex]

[tex]\leadsto\sf\:2v=120[/tex]

[tex]\leadsto\sf\:v=60\:kmph[/tex]

  • Speed of bus A = 60 kmph

Speed of bus B = (v + 5)

  • Speed of bus B = 65 kmph

Hope It Helps!

Otras preguntas