Jake answered 40 km/hr while Jenny said 45 km/hr. Who do you think got the correct answer? Show your solution. Whoever got the wrong answer, what do you think is her/his mistake?
Answers
Given : A train travels 360 km at a uniform speed .
If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey.
Jake answered 40 km/hr while Jenny said 45 km/hr.
To Find : Speed of the train
who got the correct answer
Whoever got the wrong answer, what is mistake done
Solution:
Distance = Speed * Time
Distance = 360 km
Let say speed of train = x km/hr
Time taken = 360/x hr
speed had been 5 km/hr more
Speed = x + 5 km/hr
Time Taken = 360/(x + 5)
360/x - 1 = 360/(x + 5)
=> 360 (x + 5) - x(x + 5) = 360x
=> 1800 -x² - 5x = 0
=> x² + 5x - 1800 = 0
=> x² + 45x - 40x - 1800 = 0
=> x( x + 45) - 40(x + 45) = 0
=> (x - 40) (x + 45) = 0
=> x = 40 or x = - 45
Speed can not be negative
Speed of the train is 40 km/hr
Jake answered 40 km/hr
Hence Jake got the correct answer
Jenny find the speed when it had been 5 km/hr more rather than original speed. That was the error
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Step-by-step explanation:
Distance = Speed * Time
Distance = 360 km
Let say speed of train = x km/hr
Time taken 360/x hr
speed had been 5 km/hr more
Speed= = x + 5 km/hr
Time Taken = 360/(x + 5)
360/x-1= 360/(x + 5)
=> 360 (x + 5) - x(x + 5) = 360x
=> 1800 -x² - 5x = 0 => x² + 5x - 1800 = 0
=> x² + 45x40x - 1800 = 0
=> x(x +45) - 40(x +45) = 0
=> (x - 40) (x +45) = 0
=> x = 40 or x = - 45
Speed can not be negative.
Speed of the train is 40 km/hr.