A boat traveled downstream a distance of 9090 mi and then came right back. If the speed of the current was 88 mph and the total trip took 66 hourscomma nbsp, find the average speed of the boat relative to the water.
that's & nbsp;
If the boat's speed is s mi/hr, then since time = distance/speed,
9090/(s+88) + 9090/(s-88) = 66
The solution seems unreasonable. Check for typos. Like repeated digits. Fix the typos and you will get a nicer answer.
1603 MILES PER HOUR
To find the average speed of the boat relative to the water, we need to consider the speed of the boat and the speed of the current.
Let's denote the speed of the boat relative to the water as B mph and the speed of the current as C mph.
When the boat is moving downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the boat's downstream speed is B + C mph.
When the boat is moving upstream (against the current), its effective speed is decreased by the speed of the current. Therefore, the boat's upstream speed is B - C mph.
Now, given the information:
- The total distance traveled is 9090 mi.
- The speed of the current is 88 mph.
- The total trip took 66 hours.
We can set up an equation to represent the distance traveled:
Distance downstream + Distance upstream = Total distance
(B + C) * Time downstream + (B - C) * Time upstream = 9090
We also know that the total trip took 66 hours:
Time downstream + Time upstream = Total trip time
Time downstream + Time upstream = 66
We have two equations with two unknowns, B and C. We can now solve these equations to find the average speed of the boat relative to the water.
Let's solve the equations:
1. Distance equation:
(B + C) * (66 - Time upstream) + (B - C) * Time upstream = 9090
2. Total trip time equation:
(66 - Time upstream) + Time upstream = 66
Simplifying equation 2:
66 - Time upstream + Time upstream = 66
66 = 66
This equation is always true, so it doesn't provide any additional information about B and C.
Substituting equation 2 into equation 1:
(B + C) * (66 - (66 - Time upstream)) + (B - C) * (66 - Time upstream) = 9090
(B + C) * Time upstream + (B - C) * (66 - Time upstream) = 9090
B * Time upstream + C * Time upstream + B * (66 - Time upstream) - C * (66 - Time upstream) = 9090
Simplifying the equation:
B * Time upstream + C * Time upstream + 66B - B * Time upstream - 66C + C * Time upstream = 9090
66B - 66C = 9090
B - C = 138.18 (Dividing both sides by 66)
Now, we have the value of B - C, which represents the average speed of the boat relative to the water. Therefore, the average speed of the boat relative to the water is 138.18 mph.