Increasing his speed by 2mph a person covers creation distance 1 hr early.had he decreased his speed by 2mph he would have taken 1 1/2 he late.find the distance travelled by person?
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Answer:
Distance traveled by the person is 60 miles.
Step-by-step explanation:
Let the distance traveled = D
Normal speed = s
Normal time taken = t
So, D = st
Case-1
Increased speed of the person = s+2
Decreased time taken by the person = t - 1
Hence
D = (s+2)(t-1)
=> st = st + 2t -s -2
=> 2t = s+2
Case-2
Decreased speed of the person = s-2
Increased time taken by the person = t + 3/2
Hence,
D = (s-2)(t+3/2)
=> st = st -2t + 3s/2 - 3
=> 2t = 3s/2 - 3
putting the value of 2t from the above eqn
s + 2 = 3s/2 - 3
=> s/2 = 5
=> s = 10 mph
2t = s + 2
=> 2t = 10 + 2 = 12
=> t = 6 hr
Hence distance traveled, D = st = 10 x 6 = 60 miles.
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