two automobiles left simultaneously from cities a and b heading towards each other and met in 5 hours. the speed of the automobile that left city a was 10 km/hour less than the speed of the other automobile. if the first automobile had left city a 4 1/2 hours earlier than the other automobile left city b, then the two would have met 150 km away from b. find the distance between a and b.

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step-by-step explanation:

the two cars meet at:   t = 5 hours

car a leaves at:   t = 0

car b leaves at:   t = 4.5   hours, so it only travels for 0.5   hours

car b travels 150 km

 d = distance from a to b

therefore, car a travels: d – 150 km

      150 = (vь) • (0.5)     time of travel = 0.5   hours

          vь = 300   km/h     speed of car b

                va = vь – 10

                va = 300 – 10

                va = 290   km/h     speed of car a

  d – 150 = (va) • t

    d – 150 = (290) • 5

    d = 1600   km

step-by-step explanation: