Theory question 107
Linear and Simultaneous EquationsYaro drove from a town Gaja to Banga. After 2 hours in the journey, he observed that he had covered 80 km and realized that if he continued driving at same average speed, he would end up being late for 15 minutes. If he decided to increase the average speed by 10 km/h, he would arrive at Banga 36 minutes earlier. Find the distance between Gaja and Banga.
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Model answer
Speed so far = 80 ÷ 2 = 40 km/h. Let the distance be d km and the planned time T h
At 40 km/h: d/40 = T + ¼
At 50 km/h for the rest: 2 + (d − 80)/50 = T − 36/60 = T − 0.6
Subtract: d/40 − 2 − (d − 80)/50 = 0.85 ⇒ d/200 − 0.4 = 0.85 ⇒ d = 250 km
(Check: 250/40 = 6.25 h = 6 h + 15 min; 2 + 170/50 = 5.4 h = 6 h − 36 min)
Explanation
Use the planned (on-time) journey time as the link between the two cases.