if a person rows a boat at the speed of 8 kmph and the speed of stream is 1.4 kmph then it takes 2 hrs to reach somewhere and coming back .if he increase his speed by 25 percentage how will time be affected?
Answers
Step-by-step explanation:
Statement of the given problem,
(i) If a person rows a boat at the speed of 8 km/hr and the speed of stream is 1.4 km/hr then it takes 2 hrs to reach somewhere and coming back.
(ii) If he increases his speed by 25 percent how will time be affected?
(iii) Let D denotes the one-way distance (in km) that the boat traveled.
(iv) Let T1 & T2 denote respectively initial & final total-travel times (upward and downward journey).
From (i), (iii) & (iv) we get,
D/(8 + 1.4) + D/(8 - 1.4) = T1 = 2 …… (1a)
or D/9.4 + D/6.6 = 2 or D*(5/47 + 5/33) = 2
or D*(400/1551)= 2 or D = 1551/200 = 7.755 (km) …… (1b)
From (ii), (iii) & (iv) we get,
D/(8*1.25 + 1.4) + D/(8*1.25 - 1.4) = T2
or T2 = D/11.4 + D/8.6 = 7.755/11.4 + 7.755/8.6 [from (1b)]
or T2 = 1.586 (hrs) …… (1c)
Hence from (1c) & (1a) we get,
T2/T1 = 1.586/2 = 0.793
or T2 = 0.793*T1 = (1 - 20.7/100)*T1 …… (1d)
Therefore from (1d) it is evident that
the total-travel time will be reduced by 20.7%. [Ans]