An algebra problem by edil tizon
A motorman travelled from A to B. Two hours after his leaving, he noticed that he travelled 80 km and calculated that if he had continued driving the same speed he would have been late for 15 minutes. So he increased his speed by 10km/h and arrived in B 36 minutes earlier. Find the distance between A and B in km.
The answer is 250.
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1 solution
Let denote the distance between A and B by x. He took 80km for 2 hours. His speed was V = 80/2 = 40 km/h. If he had continued the same speed he would have been late for 15 minutes, i.e. the exact time was x/40 – 15/60 h The rest of the distance was (x - 80) km. V = 40 + 10 = 50 km/h. So the time he took the distance between A and B, was 2 +(x - 80)/50 h. and it was 36 min. less than expected. Therefore the expected time was 2 + (x -80)/50 + 36/60 When we equalize the expressions for the expected time, we get the equation: x/40 – 15/60 = 2 + (x -80)/50 + 36/60 (x - 10)/40 = (100 + x - 80 + 30)/50 (x - 10)/4 = (x +50)/5 5x - 50 = 4x + 200 x = 250 So the distance between A and B is 250 km.