A motorboat can travel 35mph in still water. If the boat can travel 7 miles downstream at the same time it takes to travel 3 miles upstream, what is the rate of the river's current?

Answer: the rate of the river's current is 14 mph.

Step-by-step explanation:

Let x represent the rate of the river's current.

The speed of the motor boat in still water is 35 mph.

Since the boat travelled more miles downstream than upstream at the same time, it means that while going downstream, it moved in the direction of the current and while going upstream, it moved against the direction of the current. The total speed downstream would be

(35 + x) mph and the total speed upstream would be (35 - x) mph.

Time = distance/speed

If the boat can travel 7 miles downstream, the time spent travelling downstream is

7 / (35 + x)

At the same time it takes to travel 3 miles upstream, the time spent travelling upstream is

3 / (35 - x)

Since the time is the same, then

7 / (35 + x) = 3 / (35 - x)

Cross multiplying, it becomes

7 (35 - x) = 3 (35 + x)

245 - 7x = 105 + 3x

3x + 7x = 245 - 105

10x = 140

x = 140/10

x = 14