Question
A boat can go 3 km upstream and 5 km downstream in 55
minutes. It can also go 4 km upstream and 9 km downstream in 1 hour 25 minutes. In how much time (in hours) will it go 43.2 km downstream?Solution
Let the speed of boat and current be x km/hr and y km/hr respectively. Downstream = (x + y) km/hr Upstream speed = (x – y) km/hr According to the question 3/(x – y) + 5/(x + y) = 55/60 = 11/12 4/(x – y) + 9/(x + y) = 1 + 25/60 = 17/12 Let 1/(x + y) = a and 1/(x – y) = b 3b + 5a = 11/12 ...1) 4b + 9a = 17/12 ...2) Multiply by 4 in equation (1) and multiply by 3 in equation (2) 12b + 20a = 11/3 ...3) 12b + 27a = 17/4 ...4) Subtract equation (3) from equation (4) 7a = 17/4 – 11/3 ⇒ 7a = 7/12 ⇒ a = 1/12 ⇒ x + y = 12 km/hr Speed of downstream = 12 km/hr ∴ Time taken to cover 43.2 km distance in downstream = 43.2/12 = 3.6 hr
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