I'm having a little trouble with this problem...

Please try and walk me through the problem, too:

#1. A motorboat leaves a dock and travels at an average speed of 15 mi/h toward an island. The average speed on the return trip is 10 mi/h. How far is the island from the harbor if the total trip takes five hours?

#2. A car traveling at 88 km/h overtakes a bus traveling at 64 km/h. If the bus has a 1.5 hour head start, how far from the starting point does the car overtake the bus?

#3. A car and a bus leave the same time from the same place headed in the same direction. The average speed of the car is 30 mi/h slower than twice the speed of the bus. In 2 hours, the car is 20 mi ahead of the bus. Find the rate of the car.

Thank you so much! Any help is appreciated!

I count three problems.

#2. The bus starts out 64 x 1.5 = 96 km ahead and after the car starts, the distance between them decreases at a rate of 88-64 = 24 km/h.

Divide 96 km by 24 km/h for the answer, in hours.

Try the others yourself and someone will gladly critique your work.

#1) x=distance to the harbor

15mph/x + 10mph/x = 5 hrs

25mph/x=5hrs

25mph=5hrs(x)

x=5 miles

Just wondering... how did you get the x to the other side? And how did you get rid of the 25mph?

Thanks!

Sure! I'd be happy to help you with these problems.

#1. The key to solving this problem is to find the distance between the harbor and the island. Let's denote this distance as "d" miles.

Since the motorboat travels at an average speed of 15 mi/h toward the island, the time taken for the trip to the island is given by the equation:
time = distance / speed
t1 = d / 15

On the return trip, the average speed is 10 mi/h. Therefore, the time taken for the return trip is given by:
t2 = d / 10

It is given that the total trip takes five hours. Therefore, we can write the equation:
t1 + t2 = 5

We can substitute the values of t1 and t2 from the previous equations to get the equation:
d/15 + d/10 = 5

To solve for "d", we can multiply through by 30 (to get rid of the denominators):
2d + 3d = 150

Combining like terms, we have:
5d = 150

Dividing both sides by 5, we get:
d = 30

Therefore, the island is 30 miles away from the harbor.

#2. To solve this problem, we can start by finding the relative speed of the car in relation to the bus.
Relative speed is calculated by subtracting the speed of the bus from the speed of the car:
Relative speed = car speed - bus speed
Relative speed = 88 km/h - 64 km/h = 24 km/h

The bus has a 1.5-hour head start. Therefore, the time for the bus is given by:
time = distance / speed
t = distance / 64

The time for the car is given by:
t + 1.5 hours

Since distance is the same for both the car and the bus when the car overtakes the bus, we can set up the following equation:
(distance traveled by the bus) = (distance traveled by the car)
t * 64 = (t + 1.5) * (64 + 24)

Simplifying this equation, we get:
64t = (t + 1.5) * 88

Expanding and simplifying further:
64t = 88t + 132

Rearranging the equation and combining like terms:
88t - 64t = 132
24t = 132

Dividing both sides by 24, we get:
t = 5.5

Next, we can substitute the value of "t" back into the equation to find the distance from the starting point where the car overtakes the bus:
distance = t * 64
distance = 5.5 * 64
distance = 352 km

Therefore, the car overtakes the bus 352 km from the starting point.

#3. Let's denote the speed of the bus as "s" mi/h.

The average speed of the car is 30 mi/h slower than twice the speed of the bus. Therefore, the speed of the car can be written as:
2s - 30 mi/h

In 2 hours, the car is 20 miles ahead of the bus. We can calculate the distance traveled by the car in 2 hours using the equation:
distance = speed * time
distance = (2s - 30) * 2

The distance traveled by the bus in 2 hours is given by:
distance = speed * time
distance = s * 2

Since the car is 20 miles ahead of the bus, we can set up the equation:
(2s - 30) * 2 = s * 2 + 20

Simplifying and rearranging the equation, we get:
4s - 60 = 2s + 20

Combining like terms, we have:
4s - 2s = 20 + 60
2s = 80

Dividing both sides by 2, we get:
s = 40

Therefore, the rate of the car is 40 mi/h.

I hope this explanation helps you understand how to solve these problems! Let me know if you have any further questions.