Powerboattakes30minutes to travel 10miles downstream. The return triptakes50 minutes. What is th speed othe current

downstream speed: 10/(1/2) = 20 mi/hr

upstream speed : 10/(5/6) = 12 mi/hr

So, if te boat's speed is b and the current's speed is c,

b+c=20
b-c=12

now go figure c

To find the speed of the current, we need to first determine the speed of the boat in still water. We can then use the given information about the downstream and return trips to solve the problem.

Let's assume the speed of the boat in still water is 'B' miles per hour, and the speed of the current is 'C' miles per hour.

For the downstream trip:
Speed of the boat relative to the ground = Speed of the boat in still water + Speed of the current
= B + C miles per hour

We are given that the downstream trip takes 30 minutes (or 0.5 hours) to cover a distance of 10 miles:

Distance = Speed × Time
10 = (B + C) × 0.5

Similarly, for the return trip:
Speed of the boat relative to the ground = Speed of the boat in still water - Speed of the current
= B - C miles per hour

We are given that the return trip takes 50 minutes (or 0.83 hours) to cover a distance of 10 miles:

Distance = Speed × Time
10 = (B - C) × 0.83

Now we have a system of two equations:

0.5(B + C) = 10
0.83(B - C) = 10

Let's solve this system of equations to find the values of B and C.

First, multiply the first equation by 2 to eliminate the decimals:

(B + C) = 20

Now, let's solve these equations simultaneously:

2(B + C) = 40
0.83(B - C) = 10

Expanding and rearranging the equations:

2B + 2C = 40
0.83B - 0.83C = 10

Multiply the second equation by 12 to eliminate the decimals:

2B + 2C = 40
10B - 10C = 120

Now we have two equations without decimals:

2B + 2C = 40
10B - 10C = 120

Let's solve these equations simultaneously:

Multiply the first equation by 5 and the second equation by 1 to get the same coefficient for C:

10B + 10C = 200
10B - 10C = 120

Add these equations together:

(10B + 10C) + (10B - 10C) = 200 + 120
20B = 320

Divide both sides by 20:

B = 16

Now that we know the speed of the boat in still water is 16 miles per hour, we can substitute this value into one of the original equations to find the speed of the current:

0.5(B + C) = 10

0.5(16 + C) = 10

8 + 0.5C = 10

Subtract 8 from both sides:

0.5C = 2

Divide both sides by 0.5:

C = 4

Therefore, the speed of the current is 4 miles per hour.