Hello, I have trouble doing this problem:
Sarah can bicycle a loop around the north part of Lake Washington in 2 hours and 40 minutes. If she could increase her average speed by 1km/hr, it would reduce her time around the loop by 6 minutes. How many kilometers long is the loop?
So this is what I attempted to do:
I change the 2hours 40 min to 160 mins
then i tried changing it to hours which was 2.6666667
and i tried to plug it in
d=r*t
but then i got confused..please help me =)
Let L be the loop distance. Let V be her speed when it takes 2.6667 hours.
You have two unknowns and must combine two equations to get an answer.
At speed V + 1 , she takes 2 hours 34 minutes = 2.5667 hours
At speed V, she takes 2.6667 hours
D = V * 2.6667 = (V+1)* 2.5667
(V+1)/V = 2.6667/2.5667 = 1.03896
V + 1 = 1.03896 V
0.03896 V = 1
V = 25.67 km/h
D = 25.67 * 2.6667 = 68.4 km
Hello there! Don't worry, I'm here to help you figure out this problem with a touch of humor. So, Sarah wants to know the length of the loop, and we know that she can reduce her time around the loop by 6 minutes if she increases her speed by 1km/hr.
Let's start by converting 2 hours and 40 minutes into a single unit, minutes. So, 2 hours are 120 minutes and adding 40 minutes gives us a total of 160 minutes. Got it? Great!
Now, we'll convert this time back into hours to make things easier. We divide 160 minutes by 60 minutes in an hour, which gives us approximately 2.67 hours. Still following? Awesome!
Since we want to find the length of the loop, we need to set up an equation. Let's call the length of the loop "d" kilometers. Sarah's original speed can then be represented as "r" km/hr, and her increased speed would be "r + 1" km/hr.
According to the information given, we know that the time it takes Sarah to complete the loop at her original speed of "r" km/hr is 2.67 hours. So, we can set up the equation as:
d = r * 2.67
Now, if Sarah increases her speed by 1km/hr, she would reduce her time around the loop by 6 minutes. Since the time is in hours, we need to convert those 6 minutes into hours as well. Calculating it, 6 minutes is equal to 0.1 hours. Stay with me!
Now, we can set up a new equation based on this information:
d = (r + 1) * (2.67 - 0.1)
Now you can simplify this equation, find the value of "d," and discover the length of the loop!
Remember, math can be confusing sometimes, but hey, at least you're not juggling numbers like a clown! Keep calm, calculate on!
To solve this problem, let's break it down step-by-step:
Step 1: Convert 2 hours and 40 minutes to minutes.
Given that 1 hour has 60 minutes, we can convert the 2 hours to minutes:
2 hours * 60 minutes/hour = 120 minutes
Now add the 40 minutes:
120 minutes + 40 minutes = 160 minutes
So, Sarah takes 160 minutes to complete the loop.
Step 2: Calculate Sarah's original average speed.
We can use the formula: speed = distance / time
Let's assume the original average speed is "r" km/hr.
Using the given information:
speed = distance / time
r = distance / 160 minutes
Step 3: Calculate Sarah's increased average speed.
We are given that increasing her speed by 1 km/hr reduces her time around the loop by 6 minutes. So, her new time will be 160 minutes - 6 minutes = 154 minutes.
Using the new time, the formula becomes:
r + 1 = distance / 154 minutes
Step 4: Solving the system of equations.
We now have two equations:
1) r = distance / 160 minutes
2) r + 1 = distance / 154 minutes
We can solve this system of equations simultaneously to find the distance.
From equation 1, we can rearrange it to find the distance in terms of r:
distance = r * 160 minutes
Now substitute the value of distance from equation 1 into equation 2:
r + 1 = (r * 160 minutes) / 154 minutes
Simplifying the equation:
r + 1 = (160r) / 154
Now, cross multiply:
154(r + 1) = 160r
Expanding and simplifying:
154r + 154 = 160r
Rearranging the equation:
160r - 154r = 154
6r = 154
r = 154 / 6
r = 25.67 km/hr (rounded to two decimal places)
Step 5: Calculate the distance of the loop.
Now that we have the value of r, we can substitute it back into either equation to find the distance.
Using equation 1:
distance = r * 160 minutes
distance = 25.67 km/hr * 160 minutes
distance = 4110.79 km/minute (rounded to two decimal places)
Therefore, the length of the loop is approximately 4110.79 kilometers.
Sure, I can help you with this problem. Let's break it down step by step.
First, let's convert the time of 2 hours and 40 minutes to minutes. We can do this by multiplying 2 hours by 60 minutes (since there are 60 minutes in an hour) and then adding the 40 minutes.
2 hours × 60 minutes/hour + 40 minutes = 120 minutes + 40 minutes = 160 minutes.
So, Sarah takes 160 minutes to cycle around the loop.
Now, let's define some variables to help us solve the problem. Let the length of the loop be "d" kilometers and the original speed be "r" km/hr.
According to the problem, Sarah takes 2 hours and 40 minutes to complete the loop at her original speed. This can be expressed as:
d = r × (2 hours + 40 minutes) = r × 160 minutes.
Next, the problem tells us that if Sarah increases her average speed by 1 km/hr, she would reduce her time around the loop by 6 minutes. So, her new speed would be r + 1 km/hr, and her new time would be (2 hours + 34 minutes) or 154 minutes:
d = (r + 1) × 154 minutes.
Now we have two equations representing the length of the loop:
Equation 1: d = r × 160 minutes,
Equation 2: d = (r + 1) × 154 minutes.
To solve for the length of the loop (d), we can set the right sides of the equations equal to each other:
r × 160 minutes = (r + 1) × 154 minutes.
Now, you can solve this equation for "r". Subtract "r × 154 minutes" from both sides and simplify the equation:
6r minutes = 154 minutes.
Finally, divide both sides by 6 to solve for "r":
r = 154 minutes / 6 minutes = 25.67 km/hr (rounded to two decimal places).
Now that we have the value of "r", we can substitute it into either equation (Equation 1 or 2) to find the length of the loop (d). Let's use Equation 1:
d = r × 160 minutes = 25.67 km/hr × 160 minutes = 4112 km/min.
Therefore, the length of the loop is approximately 4112 km.