to save fuel on the 240 km trip to the cottage, the Nakamura family reduce their usual average speed by 20 km/h. this lengthens their journey by 1 hour. what is the slower average speed?
pleassee help! thanks :)
How long does it usually take them to make this trip?
oh my gosh! so my teacher handed us two versions of this question...i didn't have that answer! sorry. the proper question i will repost.
never mind it does not say. does this mean the question is complete and unable to answer? its a question on an assignment and i do not know how to answer it. should ijust say uncomplete?
Let V1 = the original average speed and V2 = the slower average speed. You have these two equations in two unknowns:
V1 - V2 = 20 (km/h)
240/V2 - 240/V1 = 1 (hour)
You want to solve for V2. Use substitution, V1 = V2 + 20
240/V2 -240/(V2 +20) = 1
240*[1/V2 - 1/(V2+20)] = 1
20/[V2(V2+20)] = 1/240
V2*(V2+20) = 4800
You can solve this as a quadratic equation and take the positive root. You should get
V2 = 60 km/h
Note that there was enough information provided to solve for both velocities, using simultaneous equations.
I LOVE MATH
While this gave me the answer, I was unable to understand how this was done. 2/10 would not math again
Also, shout out to my pears
To find the slower average speed, we need to analyze the given information. Let's break it down step by step:
1. Let's assume their usual average speed (before reducing) is "x" km/h.
2. The reduced average speed is x - 20 km/h. This means they are traveling 20 km/h slower than their usual speed.
3. The distance to the cottage is 240 km.
4. When they reduce their usual average speed by 20 km/h, the length of their journey increases by 1 hour.
Now, let's use the formula for speed, which is distance divided by time:
speed = distance / time
Their usual speed can be calculated as:
Usual speed = distance / (time without reducing speed)
Reduced speed can be calculated as:
Reduced speed = distance / (time with reducing speed)
Since we know the distance to the cottage is 240 km and the time increases by 1 hour when their speed is reduced, we can set up the following equation:
240 / (time without reducing speed) = 240 / (time with reducing speed + 1)
To solve for the slower average speed, we need to find the value of (time with reducing speed + 1). We can do this by setting up an equation:
240 / (time without reducing speed) = 240 / (time with reducing speed + 1)
Now, let's solve for (time with reducing speed + 1):
1. Cross-multiply the equation:
240 * (time with reducing speed + 1) = 240 * (time without reducing speed)
2. Distribute the multiplication on both sides:
240 * time with reducing speed + 240 = 240 * time without reducing speed
3. Subtract 240 from both sides:
240 * time with reducing speed = 240 * time without reducing speed - 240
4. Divide both sides by 240:
time with reducing speed = (240 * time without reducing speed - 240) / 240
Now, we know the time with reducing speed. Let's substitute this value back into the original equation to find the slower average speed:
Reduced speed = distance / (time with reducing speed + 1)
Reduced speed = 240 / [((240 * time without reducing speed - 240) / 240) + 1]
Simplifying further:
Reduced speed = 240 / (240 * time without reducing speed - 240 + 240)
Reduced speed = 240 / (240 * time without reducing speed)
Therefore, the slower average speed is 240 / (240 * time without reducing speed).
To calculate the specific value, you will need to determine the original time without reducing speed for the Nakamura family.