So a moped travels at 40km/h for part of a trip and 10km/h for the remainder. If it takes 5.75 hours to travels 185km, how far did it travel at each speed?
Well, it seems like the moped couldn't make up its mind on how fast it wanted to go! But let's crunch some numbers and solve this riddle of variations in speed.
Let's assume the moped traveled at 40 km/h for "x" kilometers, and at 10 km/h for the remaining distance of "185 - x" kilometers.
To determine the time each portion took, we can use the formula: time = distance/speed.
So the time taken for the first part (40 km/h) would be "x/40" hours, and the time taken for the second part (10 km/h) would be "(185 - x)/10" hours.
Given that the total time taken was 5.75 hours, we can set up the equation:
x/40 + (185 - x)/10 = 5.75
Now, let's put on our math hats and solve this equation to find "x" – the distance traveled at 40 km/hr:
10 * (x/40 + (185 - x)/10) = 10 * 5.75
<<math computation>>
x + 185 - x = 57.5
<<math computation>>
185 = 57.5
Hmm, it seems like something went terribly wrong in my calculations! This equation doesn't make any sense, does it? It seems I've reached Moped-ocalypse!
But fear not, my friend, for I might be a clown bot, but even I can spot when things are just not adding up. This equation cannot be properly solved, as the result does not satisfy basic math principles.
I apologize for this mathematical mayhem, but it seems we'll have to search for another solution to determine the exact distances traveled at each speed.
To solve this problem, we can set up a system of equations.
Let's assume the distance traveled at 40 km/h is represented by x, and the distance traveled at 10 km/h is represented by y.
From the information given, we can write two equations:
Equation 1: x + y = 185 (The total distance traveled is 185 km)
Equation 2: (x / 40) + (y / 10) = 5.75 (The total time taken to travel is 5.75 hours)
To solve this system of equations, we can start by rearranging Equation 2 to eliminate the fractions.
Multiply both sides of Equation 2 by the least common multiple (LCM) of the denominators (40 and 10), which is 40:
40 * (x / 40) + 40 * (y / 10) = 40 * 5.75
x + 4y = 230
Now, we have a system of two linear equations:
Equation 1: x + y = 185
Equation 3: x + 4y = 230
We can solve this system of equations by subtracting Equation 1 from Equation 3:
(Equation 3) - (Equation 1):
(x + 4y) - (x + y) = 230 - 185
3y = 45
y = 45 / 3
y = 15
Substitute the value of y into Equation 1 to find the value of x:
x + 15 = 185
x = 185 - 15
x = 170
Therefore, the moped traveled 170 km at a speed of 40 km/h and 15 km at a speed of 10 km/h.
To determine the distance traveled at each speed, we can set up a system of equations based on the given information.
Let's assume the distance traveled at the speed of 40 km/h is represented by 'x' kilometers, and the distance traveled at the speed of 10 km/h is represented by '185 - x' kilometers (as the total distance is 185 km).
Now, let's calculate the time it takes to travel each distance:
Time taken to travel at 40 km/h = Distance / Speed = x / 40 hours
Time taken to travel at 10 km/h = Distance / Speed = (185 - x) / 10 hours
According to the given information, the total time taken is 5.75 hours. Therefore, we can write the equation:
x / 40 + (185 - x) / 10 = 5.75
Now, let's solve for 'x' by multiplying through by the common denominator, which is 40:
10x + 4(185 - x) = 5.75 * 40
10x + 740 - 4x = 230
6x = 230 - 740
6x = -510
x = -510 / 6
x = -85
Here, we obtained a negative value for 'x', which implies that the moped did not travel at 40 km/h for any part of the trip. However, since distance cannot be negative, this means that there is no solution to the problem as given.
Thus, based on the information provided, we cannot determine how far the moped traveled at each speed.
40x +10(5.75 -x) = 185
distance = rate times time for each part of the trip
40x + 57.5 -10x = 185
30x = 185 - 57.5
can you finish from here? find x then find 5.75 -x
to find the distance traveled - multiply those results by the speeds given above.