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18 Jul 2022, 08:00
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Difficulty:
65%
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Question Stats:
65% (02:43) correct
35%
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wrong
based on 269
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Ronaldo and Messi race each other in an x-meter race. They start simultaneously from the same point. If Ronaldo, running at a constant rate, covers the distance in 8 seconds, while Messi, running at a constant rate, covers the distance in 10 seconds, in how many seconds the distance left to cover by Ronaldo is half the distance left to cover by Messi ?
A. 3 seconds
B. 10/3 seconds
C. 5 seconds
D. 20/3 seconds
E. Cannot be determined
A. 3 seconds
B. 10/3 seconds
C. 5 seconds
D. 20/3 seconds
E. Cannot be determined
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18 Jul 2022, 08:46
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Given: Ronaldo and Messi race each other in an x-meter race. They start simultaneously from the same point.
Asked: If Ronaldo, running at a content rate, covers the distance in 8 seconds, while Messi, running at a content rate, covers the distance in 10 seconds, in how many seconds the distance left to cover by Ronaldo is half the distance left to cover by Messi ?
Ronaldo: -
Distance = x meter
Time = 8 seconds
Speed = x/8 m/s
Messi: -
Distance = x meter
Time = 10 seconds
Speed = x/10 m/s
Let after t seconds, the distance left to cover by Ronaldo is half the distance left to cover by Messi
(x - xt/8) = (x- xt/10)/2
2(1-t/8) = (1-t/10)
2 - t/4 = 1 - t/10
1 = (t/4-t/10) = (5t-2t)/20 = 3t/20
t = 20/3 seconds
IMO D
Asked: If Ronaldo, running at a content rate, covers the distance in 8 seconds, while Messi, running at a content rate, covers the distance in 10 seconds, in how many seconds the distance left to cover by Ronaldo is half the distance left to cover by Messi ?
Ronaldo: -
Distance = x meter
Time = 8 seconds
Speed = x/8 m/s
Messi: -
Distance = x meter
Time = 10 seconds
Speed = x/10 m/s
Let after t seconds, the distance left to cover by Ronaldo is half the distance left to cover by Messi
(x - xt/8) = (x- xt/10)/2
2(1-t/8) = (1-t/10)
2 - t/4 = 1 - t/10
1 = (t/4-t/10) = (5t-2t)/20 = 3t/20
t = 20/3 seconds
IMO D
18 Jul 2022, 12:05
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The table denoting speed distance and time for Ronaldo and Messi is shown below -
Screenshot 2022-07-19 002723.png [ 25.47 KiB | Viewed 5638 times ]
Assume at time 't', the distance left to cover by Ronaldo is half the distance left to cover by Messi.
Distance covered by Ronaldo in 't' seconds = \(\frac{xt}{8}\)
Distance left to be covered by Ronaldo = \(x -\frac{xt}{8}\) =\(\frac{x(8-t)}{8}\)
Distance left to be covered by Messi = \(x - \frac{xt}{10}\) =\(\frac{x(10-t)}{10}\)
Given -
\(\frac{x(8-t)}{8}\) = \(\frac{1}{2}\)*\(\frac{x(10-t)}{10}\)
Upon simplifying
t = 20/3
IMO D
Attachment:
Screenshot 2022-07-19 002723.png [ 25.47 KiB | Viewed 5638 times ]
Assume at time 't', the distance left to cover by Ronaldo is half the distance left to cover by Messi.
Distance covered by Ronaldo in 't' seconds = \(\frac{xt}{8}\)
Distance left to be covered by Ronaldo = \(x -\frac{xt}{8}\) =\(\frac{x(8-t)}{8}\)
Distance left to be covered by Messi = \(x - \frac{xt}{10}\) =\(\frac{x(10-t)}{10}\)
Given -
\(\frac{x(8-t)}{8}\) = \(\frac{1}{2}\)*\(\frac{x(10-t)}{10}\)
Upon simplifying
t = 20/3
IMO D
