Find the downstream distance travelled by boat B, if the time taken to cover upstream distance is 10 hours?

Solution

x²   – 31x + 220 = 0 Factors of 220 which satisfies the above equation are 20 and 11 x² – 11x – 20x + 220 = 0 x(x – 11) – 20(x – 11) = 0 (x – 11) × (x – 20) = 0 x = 11 or 20 Half of the larger root is the speed of boat B in still water. Speed of boat B in still water = 10 km/hr Let speed of stream = x km/hr Upstream speed = (10 – x) km/hr Downstream speed = (10 + x) km/hr Total time taken by boat B to cover the complete distance = 16 hours Time taken by boat B to cover upstream distance = 10 hours (given) So, time taken by boat B to cover downstream distance = 6 hours Upstream distance travelled by boat B = 52.6% of total distance = of Total Distance So, downstream distance travelled by boat B = of Total Distance Let, total distance travelled by boat B = d kms According to the question,   From equation (1) & (2) we get, 19 × 3 (10 - x) = 19 × 2 (10 + x) On solving, we get, x = 2 km/hr So, downstream speed of boat B = 12 km/hr Time taken by boat B to travel downstream distance = 6 hours Downstream distance travelled by boat B = (12 × 6) kms = 72 kms Hence, option 4 is the correct answer.