a boat traveled against the current for 70 miles for the sane time it traveled with the current for 95 miles. what was the boats average speed if the rate of the current was 5 mi/h?

since time = distance/speed, if the boat's speed was s, then

70/(s-5) = 95/(s+5)
s = 33

avg speed = totaldistance/totaltime
= (70+95)/(70/28 + 90/38)
= 1254/37 or 33.89 mi/hr

To find the boat's average speed, we need to calculate the time it took for each leg of the trip.

Let's assume the boat's speed in still water (without any current) is represented by "x" miles per hour.

When traveling against the current, the effective speed of the boat will be reduced by the speed of the current. So, the boat's effective speed is (x - 5) miles per hour.

Similarly, when traveling with the current, the effective speed of the boat will be increased by the speed of the current. So, the boat's effective speed is (x + 5) miles per hour.

Now we can use the formula: distance = speed × time

For the leg of the trip against the current:
70 = (x - 5) × time

For the leg of the trip with the current:
95 = (x + 5) × time

Since the time is the same for both legs, let's solve the first equation for time:
time = 70 / (x - 5)

Substitute this value of time into the second equation:
95 = (x + 5) × (70 / (x - 5))

Now, we can solve for x:
95(x - 5) = 70(x + 5)

Distribute on both sides:
95x - 475 = 70x + 350

Combine like terms:
95x - 70x = 350 + 475
25x = 825

Divide by 25 on both sides:
x = 33

So, the boat's speed in still water is 33 miles per hour.

The average speed of the boat can be found by taking the average of the effective speeds (against and with the current):
Average speed = (x - 5 + x + 5) / 2
Average speed = (33 - 5 + 33 + 5) / 2
Average speed = 66 / 2
Average speed = 33

Therefore, the boat's average speed is 33 miles per hour.

To find the boat's average speed, you need to calculate its speed in still water first.

Let's assume the boat's speed in still water is represented by B (in miles per hour) and the current's rate is represented by C (in miles per hour). The boat travels against the current for 70 miles, so the effective speed is reduced by the current: B - C. Similarly, when the boat travels with the current for 95 miles, the effective speed is increased by the current: B + C.

Since distance = speed × time, we can set up two equations based on the given information:

70 = (B - C) × t (Equation 1)
95 = (B + C) × t (Equation 2)

We can then solve these two equations simultaneously to find the boat's speed in still water, B.

Let's start by solving Equation 1 for t:
t = 70 / (B - C)

We can substitute this value of t into Equation 2:
95 = (B + C) × (70 / (B - C))

To simplify, we can cross multiply:
95(B - C) = 70(B + C)

Expanding the equation:
95B - 95C = 70B + 70C

Now, let's isolate the B term by moving 70B to the left side and 95C to the right side:
95B - 70B = 70C + 95C
25B = 165C

Divide both sides by 25:
B = (165C) / 25
B = 6.6C

Given that the rate of the current (C) is 5 mi/h, substitute this value into the equation to find B (speed of the boat in still water):
B = 6.6C
B = 6.6 * 5
B = 33

Therefore, the boat's speed in still water, or the average speed of the boat, is 33 miles per hour.