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?
Answer & explanation
Correct answer: option 1
We know that,
Downstream speed = (x + y) km/hr
Upstream speed = (x – y) km/hr
If we let the speed of the boat = x and
speed of the stream = y
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
Time taken to cover 43.2 km distance in downstream = 43.2/12 = 3.6 h