A motorboat can maintain a constant speed of 24 mph relative to the water. The boat makes a trip upstream to a certain point in 62 minutes. the return trip takes 34 minutes. What is the speed of the current?

d1 = d2,

(24-Vc)1.0333 = (24+Vc)0.5666,
24.8 - 1.033Vc = 13.6 + 0.5666Vc,
-1.0333Vc -0.5666Vc = 13.6 -24.8,
-1.6Vc = -11.2,
Vc = 7mi/h.

d1 = Distance upstream.
d2 = Distance downstream.
Vc = Velocity of the current.

To find the speed of the current, we can set up a system of equations based on the information given.

Let's assume the speed of the current is represented by 'c', and the speed of the boat in still water is represented by 'b'.

When the boat is going upstream (against the current), its effective speed decreases. Therefore, we can set up the equation:

b - c = d1 / t1
where d1 is the distance traveled upstream and t1 is the time taken (62 minutes).

Similarly, when the boat is going downstream (with the current), its effective speed increases. So we have:

b + c = d2 / t2
where d2 is the distance traveled downstream and t2 is the time taken (34 minutes).

Given that the boat can maintain a constant speed of 24 mph relative to the water, we can substitute b with 24 in both equations:

24 - c = d1 / t1
24 + c = d2 / t2

To solve this system of equations, we need to eliminate one variable. We can do this by multiplying the first equation by t2 and the second equation by t1:

24t2 - ct2 = d1
24t1 + ct1 = d2

Since the distances traveled upstream and downstream are the same (as it is a round trip), d1 = d2. So we can rewrite the equations as:

24t2 - ct2 = 24t1 + ct1

Now we can substitute the values from the problem statement into this equation. Given that t1 = 62 minutes and t2 = 34 minutes:

24 * 34 - c * 34 = 24 * 62 + c * 62

816 - 34c = 1488 + 62c

Rearranging the equation to isolate 'c', we get:

62c + 34c = 1488 - 816

96c = 672

c = 672 / 96

c = 7

Therefore, the speed of the current is 7 mph.