You jog at 9.5 km/h for 7.0km , then you jump into a car and drive an additional 16km . With what average speed must you drive your car if your average speed for the entire 23km is to be 22 km/h?
Work: i tried setting up a proportion and setting it to each other using the velocity formula but i got the question wrong so I want to know how to start. thanks
time for phase 1 = 7/9.5 = .737 hr
time for entire trip = 23/22 = 1.045 hr
time for 16 km = 1.045 - .737
= .308 hr
speed for 16 km = 16/.308 = 52 km/hr
Well, well, well! Looks like you're in a bit of a pickle! Don't worry, I'm here to help you out with a sprinkle of laughter along the way!
To start solving this problem, let's break it down into two parts: the jogging part and the driving part. We'll call the average speed during jogging "J" and the average speed during driving "D".
Now, for the jogging part, we know that you jog for a distance of 7.0 km at a speed of 9.5 km/h. So the time taken for jogging ("Tj") can be found using the formula Tj = Distance/Speed. Plugging in the values, we get Tj = 7.0/9.5.
Next, for the driving part, we know that you drive for an additional 16 km at an unknown average speed D. So the time taken for driving ("Td") can be found using the formula Td = Distance/Speed. Plugging in the values, we get Td = 16/D.
Now, to find the average speed for the entire 23 km journey, we need to set up a proportion. The total time ("T") can be calculated by adding the jogging time and the driving time, T = Tj + Td.
The total distance is 23 km, and the average speed is 22 km/h. So we can set up the proportion: T = 23/22.
Now, let's substitute the values of Tj and Td into the equation for T:
23/22 = (7/9.5) + (16/D).
To solve this equation, we can cross-multiply and solve for D. But hey, it's always better to add a little humor to the mix, right? So let me tell you a joke while you do the math!
Why was the math book sad?
Because it had too many problems. 😉
Okay, back to solving. Cross-multiplying the equation, we have:
23D = 22 * [(7/9.5) + (16/D)].
Now, simplify and solve for D. Once you find the value of D, you'll have the average speed at which you must drive your car.
Remember, math is never too serious when you've got a clown bot by your side! Good luck!
To solve this problem, we can calculate the total time it takes to cover the entire distance (23 km) at an average speed of 22 km/h.
Let the average speed of the car be x km/h.
The time taken to jog the first 7 km is given by: time = distance / speed = 7 km / 9.5 km/h = 0.74 hours.
The time taken to drive the next 16 km at x km/h is given by: time = distance / speed = 16 km / x km/h = 16/x hours.
The total time taken to cover the entire distance is given by the sum of these two times (0.74 + 16/x) hours.
Since average speed is calculated as total distance / total time, we can set up the equation:
Average speed = Total distance / Total time
22 km/h = 23 km / (0.74 + 16/x) hours.
Now, we can solve this equation to find the value of x.
To do this, cross multiply:
22 km/h * (0.74 + 16/x) hours = 23 km
Simplify:
22 * (0.74 + 16/x) = 23
Distribute:
16.28 + 352/x = 23
Subtract 16.28 from both sides:
352/x = 6.72
Multiply both sides by x:
352 = 6.72x
Divide both sides by 6.72 to solve for x:
x = 52.38 km/h
Therefore, you must drive your car at an average speed of 52.38 km/h to maintain an overall average speed of 22 km/h for the entire 23 km.
To solve this problem, you can use the concept of average speed and the formula: Average Speed = Total Distance/Total Time.
Let's break down the problem into two parts: the jogging portion and the driving portion.
1. Jogging portion:
Distance covered = 7.0 km
Speed during jogging = 9.5 km/h
The time taken for jogging can be found by dividing the distance by the speed: Time = Distance/Speed
Time taken for jogging = 7.0 km / 9.5 km/h
2. Driving portion:
Distance covered = 16 km
Speed during driving = unknown (let's call it "v" km/h)
The time taken for driving can be found by dividing the distance by the speed: Time = Distance/Speed
Time taken for driving = 16 km / v km/h
Now, let's consider the total distance and total time for the entire journey:
Total distance = 7.0 km (jogging) + 16 km (driving) = 23 km
Total time = Time taken for jogging + Time taken for driving
To find the average speed for the entire journey, we can use the formula:
Average Speed = Total Distance/Total Time
We know that the average speed for the entire journey should be 22 km/h. Therefore, we can set up the equation:
22 km/h = 23 km / (Time taken for jogging + Time taken for driving)
Now, we can substitute the known values:
22 km/h = 23 km / ((7.0 km / 9.5 km/h) + (16 km / v km/h))
Simplifying further:
22 km/h = 23 km / (7.0/9.5 + 16/v)
To solve for "v," the average speed during driving, you can cross-multiply and solve the equation:
(7.0/9.5 + 16/v) = 23/22
After solving this equation, you should find the value of "v," which represents the average speed you need to drive your car for the entire 23 km to achieve an average speed of 22 km/h.