Speed and time problem, confusing and tricky !

Question

a bus left townA and travelled towards townC at uniform speed. At 11.00am when the bus was 40 km from townA, a car left townC and travelled towards townA. When the car reached townA at 3.00pm, the bus had only covered 90% of its journey. Find the speed of the car if it was 19 km/h faster than the bus.

 

please provide some working out answer, thank you in advance ...

Answer 1

Let x = speed of car  Then, x-19 = speed of bus

 

The car traveled 4 hours to get from A to C.  

 

   Distance = (Rate)(Time)

 

   So, distance from A to C = 4x

 

Distance traveled by the bus by 3 PM

 

                                     = 40 + 4(x-19)

 

                                     = 90% of the distance from A to C

 

                                     = 0.9(4x) = 3.6x

 

So, 40 + 4(x-19) = 3.6x

 

      40 + 4x - 76 = 3.6x

 

                  -36 = -0.4x     x = 36/0.4 = 90 km/hr ≈55.8 miles/hr

 

 

Answer 2

My interpretation:

x=distance from A to C

v=speed of car

t=time of car trip from A to C

t=4hrs

Car: x=v*t=4*v

Bus: (v-19)*t=.9x-40, the car is 19km faster than the bus, and the bus cover 90% of the journey in 4hrs and had already travelled 40km when the car started.

The simultaneous solution to the two equations gives x=360km

therefore since v=x/t = 360km/4hrs.

So, v=90km/hr for the car.  The bus is 19km slower, so its speed is 71km/hr.

 

Answer 3

1. Distance D = Rate * Time
2. At 3:00PM  { four hours later}
1. D  = R_C*T   {D is the total distance from town A to town C.  R_C refers to the rate/speed of car}
2. D =  4R_C   {Eqn 1}
3. D_B =  0.9D   {Eqn 2.    D_B is the distance traveled by the bus}
4. D_B-40 = 4R_B   {Eqn 3.  Note that 40km is subtracted because the bus had already traveled 40km by 11AM}
3. Rate/speed of car is 19km/hr faster
1. Rc = R_B + 19  {Eqn 4}
4. We now have 4 equations, and four unknowns {D, R_C, D_B, and R_B}.  So we can solve this problem using substitution method, and find the speed of the car (R_C).  I will leave this part of the problem to you to solve.
5. You should get RC = 90 km/hr.  And therefore RB = 71 km/hr.  Make sure to doublecheck your answer.