Question

Amirah travels by coach from Singapore to Penang, which are 700 km apart, to visit her grandparents. She returns to Singapore by car at an average speed which is 30 km/hr greater than that of a coach.

1) If the average speed of the car is x km/h and the time taken for the whole journey is 20 hours, formulate an equation in x and show that it reduces to x^2-100x+1050=0

2) Solve the equation x^2-100x+1050=0, giving both your answers correct to 2 decimal places.

3) Find the time taken for the return journey

Answer 1

Part 1:

700/x + 700/(x - 30) = 20

700(x - 30) + 700x = 20(x² - 30x)

35(x - 30) + 35x = x² - 30x

35x - 1,050 + 35x = x² - 30x

70x - 1,050 = x² - 30x

x² - 100x + 1,050 = 0

Part 2:

x = (100 ± √(100² - 4(1)(1,050)))/2

= (100 ± √5,800)/2

= (100 ± 10√58)/2

= 50 ± 5√58

= 11.92, 88.08

Part 3:

By coach: 55.08 km/h

By car: 88.08 km/h