Question
The speed of boat 'X' in upstream is 18 km/hr and speed
of boat 'Y' in downstream is 30 km/hr. If the difference between speeds of boat 'X' and 'Y' in still water is 20 km/hr, then find the time taken by boat 'X' to cover 210 kilometres in downstream. (Note: speed of boat 'X' in still water is more than that of boat 'Y' and both boats are travelling in same river)Solution
ATQ,
Let speed of boat 'X' in still water be 'x' km/hr Therefore, speed of boat 'Y' in still water = (x - 20) km/hr According to the question, (x - y) = 18 ...... (I) And, (x - 20) + y = 30 Or, (x + y) = 50 ...... (II) Adding equation (I) and (II), we get 2x = 68 Or, 'x' = (68 / 2) = 34 Putting value of 'x' in equation (I), we get 'y' = 16 Therefore, downstream speed of boat 'X' = 34 + 16 = 50 km/hr Required time taken = (210 / 50) = 4.2 hours
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