In a race, X beats Y by 50 second. In the same race, Y beats Z by 70 seconds. Y's speed is the average of the speeds of X and Z. The time (in minutes) taken by Y to run the race is:
Answers
ans:5(5/6) or 35/6
Happy learning answer is in the photo shared
Given : In a race, X beats Y by 50 second.
In the same race, Y beats Z by 70 seconds.
Y's speed is the average of the speeds of X and Z.
To Find : The time (in minutes) taken by Y to run the race is:
Solution:
X beats Y by 50 second. In the same race, Y beats Z by 70 seconds.
x completes the race in t sec
y completed the race in t + 50 secs
z completed the race in t + 50 + 70 = t + 120 secs
Distance = D
Y's speed is the average of the speeds of X and Z.
=> 2 ( D/(t + 50)) = D/t + D/(t + 120)
=> 2/(t + 50) = 1/t + 1/(t + 120)
=> 2/(t + 50) = (2t + 120)/t (t + 120)
=> t (t + 120) = ( t + 60) ( t + 50)
=> t² + 120t = t² + 110t + 3000
=> 10t = 3000
=> t = 300
y completed the race in t + 50 secs = 300 + 50 = 350 sec
Time in mins = 350/60 = 35/6 mins
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