Answer:
rate of the current = 2 km/hr
Step-by-step explanation:
d = rt
Let c = rate of the current
Rate of boat downstream = 10 + c
Time going downstream = 24/(10 + c)
Rate of boat upstream = 10 - c
Time going upstream = 24/(10 - c)
Since the total time is 5 hr, then
24/(10 + c) + 24/(10 - c) = 5
24(10 - c) + 24(10 + c) = 5(10 + c)(10 - c)
240 - 24c + 240 + 24c = 500 - 5c^2
480 = 500 - 5c^2
5c^2 = 20
c^2 = 4
c = 2 or -2
Since a rate cannot be negative, the rate of the current = 2 km/hr
