Answer:
x = 5 mph
the rate of the boat in still water is 5 mph.
Step-by-step explanation:
Let x represent the speed of the boat in still water;
Given that the rate of the current is 3 mph.
When it is traveling against current, its relative speed is;
v1 = x - 3
When it is traveling with current, its relative speed is;
v1 = x + 3
Given;
A boat can travel 10 miles against a current in the same time that it can travel 40 miles with the current.
d1 = 10 miles
d2 = 40 miles
Distance = speed × time
time = distance/speed
The time taken for both cases are the same t;
t = d1/v1 = d2/v2
d1/v1 = d2/v2
Substituting the values;
10/(x-3) = 40/(x+3)
Cross multiply;
10(x+3)= 40(x-3)
10x + 30 = 40x - 120
Collecting the like terms;
40x -10x = 120+30
30x = 150
x = 150/30
x = 5 mph
the rate of the boat in still water is 5 mph.
