I can't figure this one out
During a trip, a canoe travles 47 miles at r speed. The second part of the trip the canoe travels 9 miles, but 5 mph slower. The total trip is 5 hrs. What is the speed of each part of the trip?
I start with 47/r+9/r-5=5hrs
Then I multiply both sides by the LCD?
r(r-5)(47/r+9/r-5)=5
47(r-5)+9r=5r(r-5)
47r-???+9r=3r^2? I am lost here
Maybe-
47x5r=235?
47r-235+9r=5r-4r?
Quadratic-
5r^2-60r+235=0???
You have it figured out.
47(r-5)+9r=5r(r-5)
47r-235+9r=5r^2-25r
Rearranging and combining you had an error.
I got 5r^2-81r+235=0
Solve using the quadratic formula. One of the solutions of the quadratic will be less than 5 which would imply that the canoe would change directions for the (r-5) rate.
start with 47/r+9/r-5=5hrs OK to here. I will rewrite to see it more clearly.
[47/r] + [9/(r-5)] = 5
multiply both sides by r(r-5) to get
47(r-5) + 9r = 5(r)(r-5)
47r - 235 + 9r = 5r^2 - 25r
47r - 235 + 9r -5r^2 + 25r = 0
-5r^2 + 81r -235 = 0
I changed the sign here but it isn't necessary.
5r^2 -81r + 235 = 0
and solve by the quadratic formula. I et r = 12.4 and if I remember the problem that is mph. Then r-5 = 7.4 mph.
I hope this helps.
Then I multiply both sides by the LCD?
r(r-5)(47/r+9/r-5)=5
47(r-5)+9r=5r(r-5)
47r-???+9r=3r^2? I am lost here
Maybe-
47x5r=235?
47r-235+9r=5r-4r?
Quadratic-
5r^2-60r+235=0???
I GOT IT!!!!! THANK YOU!!! THANK YOU!!! THANK YOU!!!
hi quidditch!!! remember me??
To solve the problem, let's break it down step by step.
Step 1: Define the variables
Let's assume that the speed for the first part of the trip (47 miles) is 'r' mph. Then, the speed for the second part of the trip (9 miles) would be 'r-5' mph since it is 5 mph slower.
Step 2: Set up the equation
The total time for the trip is given as 5 hours. We can create an equation using the formula: speed = distance / time.
For the first part of the trip:
Time = Distance / Speed
Time = 47 miles / r mph
Time = 47/r
For the second part of the trip:
Time = Distance / Speed
Time = 9 miles / (r - 5) mph
Time = 9/(r - 5)
Since the total trip takes 5 hours, the sum of the times for both parts should be equal to 5:
47/r + 9/(r - 5) = 5
Step 3: Solve the equation
To solve the equation, let's find a common denominator and multiply both sides by it. The common denominator in this case is (r)(r - 5).
(r)(r - 5)(47/r) + (r)(r - 5)(9/(r - 5)) = (r)(r - 5)(5)
Simplifying the equation:
47(r - 5) + 9r = 5r(r - 5)
Step 4: Simplify and solve the quadratic equation
Expand and combine like terms:
47r - 235 + 9r = 5r^2 - 25r
56r - 235 = 5r^2 - 25r
Rearrange the equation in standard quadratic form:
5r^2 - 25r - 56r + 235 = 0
5r^2 - 81r + 235 = 0
Now, you can solve this quadratic equation using factoring, completing the square, or the quadratic formula.
If you use the quadratic formula, the equation becomes:
r = (-(-81) ± √((-81)^2 - 4(5)(235))) / (2(5))
Simplify this equation to find the values of 'r' that make the equation true.