Question
A car travels from town P to town Q and back. The
distance between P and Q is 240 km. On the onward journey (P to Q), the speed of the car is 20 km/h more than on the return journey. The total time taken for the whole trip is 10 hours. What is the speed of the car from P to Q?Solution
Let speed on return (Q to P) = v km/h. Then onward speed (P to Q) = v + 20 km/h. Time from P to Q = 240 / (v + 20) Time from Q to P = 240 / v Total time = 10 hours: 240/(v + 20) + 240/v = 10 Multiply by v(v + 20): 240v + 240(v + 20) = 10v(v + 20) 240v + 240v + 4800 = 10v² + 200v 480v + 4800 = 10v² + 200v Rearrange: 10v² + 200v - 480v - 4800 = 0 10v² - 280v - 4800 = 0 Divide by 10: v² - 28v - 480 = 0 Discriminant = 28² + 4×480 = 784 + 1920 = 2704 = 52² v = (28 ± 52) / 2 → positive root = (28 + 52)/2 = 80/2 = 40 So return speed = 40 km/h Onward speed = v + 20 = 60 km/h
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