15. 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/h greater than that of a coach.
(i) 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 x2 – 100x +1050 = 0.
(ii) Solve the equation x? - 100x +1050 = 0, giving
both your answers correct to 2 decimal places.
(iii) Find the time taken for the return journey.
Answers
Given : 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/h greater than that of a coach.
If the average speed of the car is x km/h and the time taken for the whole journey is 20 hours,
To Find : formulate an equation in x and show
that it reduces to x² – 100x +1050 = 0.
(ii) Solve the equation x²- 100x +1050 = 0, giving both your answers correct to 2 decimal places.
(iii) Find the time taken for the return journey.
Solution:
Distance one way = 700 km
speed of the car x km/h
Speed of coach = x - 30 km./hr
Time = 700/x + 700/(x - 30) = 20
=> 35/x + 35/(x - 30) = 1
=> 35( x- 30 + x) = x(x - 30)
=> 70x - 1050 = x² - 30x
=> x² - 100x + 1050 = 0
x = (100 ± √100² - 4(1)(1050) )/2
=> x = 88.08 or 11.92 x must be greater than 30
Hence x = 88.08
Speed of car = 88.08 km/hr
time taken for the return journey. = 700/88.08 = 7.947 hrs
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