Answer: the current of the river is 3 mph.
Step-by-step explanation:
Let x represent the current of the river.
The boat travels 2.4 miles downstream. Assuming it travelled with the current of the river. If the boat travels at an average speed of 21 miles per hour in the still water, it means that the total speed at which the boat travelled downstream is
(21 + x) mph
Time = distance/speed
Time taken to travel downstream is
2.4/(21 + x)
it travels 1.8 miles upstream. Assuming it travelled against the current of the river. it means that the total speed at which the boat travelled upstream is
(21 - x) mph
Time taken to travel upstream is
1.8/(21 - x)
Since the time taken to travel upstream and downstream is the same, then
2.4/(21 + x) = 1.8/(21 - x)
Cross multiplying, it becomes
2.4(21 - x) = 1.8(21 + x)
50.4 - 2.4x = 37.8 + 1.8x
2.4x + 1.8x = 50.4 - 37.8
4.2x = 12.6
x = 12.6/4.2
x = 3 mph
