SOLUTION: 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 per hour great
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Question 1123073: 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 per hour greater than that of a coach.
i) if the average speed of the car is X kilometre per hour 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
ii) solve equation x ^2-100x+1050=0
iii) find the time taken for the return journey. Found 2 solutions by rothauserc, MathTherapy:Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! rate of car is x and rate of coach is x-30
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we use rate * time = distance
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let t1 be the time for the car to travel the 700 miles and t2 be the time it takes the coach to travel 700 miles
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we know that
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t1+t2 = 20 hours, then
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t2 = 20-t1
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we have two equations in two unknowns
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1) x * t1 = 700
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2) (x-30) * (20-t1) = 700
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equation 2 becomes the following after multiplying the left side of =
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20x-600-xt1+30t1 = 700
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simplifying we have
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30t1-xt1 = 1300-20x, and
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t1 = (1300-20x)/(30-x)
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substitute for t1 in equation 1
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x * (1300-20x)/(30-x) = 700
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1300x-20x^2 = 21000-700x
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20x^2 -2000x +21000 = 0
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x^2 -100x +1050 = 0
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use the quadratic formula to solve for x
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x = (-(-100) +square root((-100)^2 -4*1*1050))/(2*1) = 88.0789 Km/hr
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x = (-(-100) -square root((-100)^2 -4*1*1050))/(2*1) = 11.9211 Km/hr
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remember that x is the rate for the car and x-30 is the rate for the coach
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therefore 11.9211 Km/hr can not be the rate for the car and
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the rate for the car is 88.0789 Km/hr
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88.0789 * t1 = 700
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t1 = 700/88.0789 = 7.9474
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return trip took 7.9474 hours
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You can put this solution on YOUR website!
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 per hour greater than that of a coach.
i) if the average speed of the car is X kilometre per hour 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
ii) solve equation x ^2-100x+1050=0
iii) find the time taken for the return journey.
This was done about a week ago. Why have you reposted it? Wasn't the solution good enough for you? SOLUTION HERE =====> Travel_Word_Problems/1122780: <======= SOLUTION HERE
