A post man has to go daily from M to N in a given time. If he goes 2 and 1/2 Km per hour faster than his original speed he arrives N half an hour before the time.If he goes 2 and 1/2 Km Per Hour slower he arrives an hour later.Find the original speed and the distance from M to N. Pls Give me the right answer with explanation.
Answers
Answer:
A post man has to go daily from M to N in a given time.if he goes 2and 1/2km per hour faster than his original speed is 2/4
Answer:
distance = 15 kilometres
original speed = 7.5 kilometres
original time = 2 hours
Step-by-step explanation:
let original speed from M to N be "s" km/hr
let original time taken to travel from M to N be "t" hours
distance from point M to N = speed x time = st
we know that distance = speed x time
and distance from M to N remains same
1st case - Postman goes 2 and 1/2 Km per hour faster than his original speed and he arrives at N half an hour before the time
speed is 2.5 km/hr faster than original speed
time is 0.5 hour less than original time
distance = speed x time
=> st = ( s + 2.5 ) ( t - 0.5 )
= > st = st - 0.5s + 2.5t - 1.25
=> st - st = 2.5t - 0.5s - 1.25
=> 2.5t - 0.5s - 1.25 = 0 ----------------------> equation 1
2nd case - Postman goes 2 and 1/2 Km per hour slower than his original speed and he arrives at N one hour after the time
speed is 2.5 km/hr slower than original speed
time is 1 hour more than original time
distance = speed x time
=> st = ( s - 2.5 ) ( t + 1 )
= > st = st + 1s - 2.5t - 2.5
=> st - st = 1s - 2.5t - 2.5
=> 1s - 2.5t - 2.5 = 0
=> - 2.5t + 1s - 2.5 = 0 ----------------------> equation 2
adding equation 1 and equation 2 :
2.5t - 0.5s - 1.25 = 0
( + ) -2.5t + 1s - 2.5 = 0
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= 0 + 0.5s - 3.75 = 0
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=> 0.5s = 3.75
=> s = 3.75 / 0.5
= 7.5
the original speed is 7.5 km/hr
applying s = 7.5 in equation 1 :
2.5t - 0.5s - 1.25 = 0 ----------------------> equation 1
=> 2.5t - 0.5 ( 7.5 ) - 1.25 = 0
=> 2.5t = 0 + 1.25 + 0.5 ( 7.5 )
=> 2.5t = 5
=> t = 5 / 2.5
= 2
the original time is 2 hours
distance between M and N = original speed x original time
= 7.5 x 2
= 15
therefore the postman has to travel 15 kilometres between M and N
the original speed is 7.5 kilometres per hour
the original time is 2 hours