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 hours 25 minutes. In how much time (in hours) will it go 43.2 km downstream?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 3.6.
| Understanding/Application |
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Let the speed of the boat in still water be x and the speed of the stream be y. Downstream speed = (x+y) Upstream speed = (x-y) 3/(x-y) + 5/ (x+y) = 55/60 = 11/12 let, 1/(x-y) = b and 1/(x+y) = a 5a +3b = 11/12 60a + 36b = 11 …… (1) 4b + 9a = 85/60 = 17/12 48b + 108a = 17 ...…(2) |
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Multiply equation 1 by 4 and equation 2 by 3 - 240a + 144b = 44 …..(3) 324a + 144b = 51 ..(4) subtracting eq (4) and eq(3) - 84a = 7 a = 1/12 b = 2/12 = 1/6 x+y = 12 x- y = 6 x = 9 km/h y =3 km/h Time taken to go 43.2 km downstream = 43.2 /12 = 3.6 hours |