A car can cover a ‘2d’ km distance at the speed of ‘B’ km/h in 30 hours. The speed of the boat in still water and the speed of the stream are ‘B’ and ‘C’ respectively. The total time taken by the boat to cover ‘d’ km distance in upstream and the same distance in downstream is 40 hours. The time taken by the boat to cover 1080 km distance in downstream is 8 hours less than the time taken by the boat to cover 600 km distance in upstream. Find out the time taken by the boat to cover (d-210) km distance in still water which is given in the form of equations below. Identify which of the following equations denotes the correct time?

(i) [{C(B+C)}/5B] + 1.5

(ii) [{C(B-C)}/B] - 3.5

(iii) [18B/{C(B-C)}] + 10.3

Solution

A car can cover a ‘2d’ km distance at the speed of ‘B’ km/h in 30 hours. 2d/B = 30 d/B = 15 d = 15B    Eq.(i) The total time taken by the boat to cover ‘d’ km distance in upstream and the same distance in downstream is 40 hours. [d/(B-C)] + [d/(B+C)] = 40 Put Eq.(i) in the above equation. [15B/(B-C)] + [15B/(B+C)] = 40 By solving the above equation, 30B ² = 40B ² − 40C ² 40C ² = 40B ² − 30B ² 40C ² = 10B ² B ² = 4C ² So B = 2C    Eq.(ii) The time taken by the boat to cover 1080 km distance in downstream is 8 hours less than the time taken by the boat to cover 600 km distance in upstream. [1080/(B+C)] = [600/(B-C)] - 8 [600/(B-C)] - [1080/(B+C)] = 8   Put the value of ‘B’ from Eq.(ii) in the above equation. [600/(2C-C)] - [1080/(2C+C)] = 8 [600/C] - [1080/3C] = 8 [600/C] - [360/C] = 8 [240/C] = 8 C = 30 km/h Put the value of ‘C’ in Eq.(ii). B = 2x30 B = 60 km/h Put the value of ‘B’ in Eq.(i). d = 15x60 = 900 km Time taken by the boat to cover (d-210) km distance in still water = (d-210)/B = (900-210)/60 = 690/60 = 11.5 hours (i) [{C(B+C)}/5B] + 1.5 Put the values of ‘B’ and ‘C’ in the above equation. [{30(60+30)}/5x60] + 1.5 [{30x90}/300] + 1.5 9 + 1.5 10.5 The above given equation is not correct. Because the required time is not obtained from it. (ii) [{C(B-C)}/B] - 3.5 Put the values of ‘B’ and ‘C’ in the above equation. [{30(60-30)}/60] - 3.5 [{30x30}/60] - 3.5 15 - 3.5 11.5 The above given equation is correct. Because the required time is obtained from it. (iii) [18B/{C(B-C)}] + 10.3 Put the values of ‘B’ and ‘C’ in the above equation. [(18x60)/{30(60-30)}] + 10.3 [1080/{30x30}] + 10.3 [1080/90] + 10.3 12 + 10.3 22.3 The above given equation is not correct. Because the required time is not obtained from it.