in his spare time, kim likes to go cycling. he cycles partly on paved surfaces and partly off-road, through hilly and wooded areas. he cycles at 25km/hon paved surfacesand at 10 km/h off-road. one day, he cycled 41km in 2h. how far did he cycle off road?
Cycled X-hrs on paved surfaces.
Cycled Y-hrs off-road.
=
Eq1: X + Y = 2 hrs.
Eq2: 25X + 10Y = 41km.
Multiply Eq1 by -10 and add Eq1 and Eq2.
-10X -10Y = -20,
25X + 10Y = 41,
Sum: 15X + 0 = 21,
X = 1.4 hrs on paved roads.
Substitute 1.4 for X in Eq1:
1.4 + y = 2,
y = 0.6 hrs off-road.
d = Vt = 10km/h * 0.6h = 6km off-road.
thanks :)
Well, Kim seems to be quite the adventurer on his bike, huh? Let's figure out how far he cycled off-road.
We know that Kim cycled a total of 41km in 2 hours. So, let's assume he spent x kilometers off-road.
If he spent x kilometers off-road, he must have cycled (41 - x) kilometers on paved surfaces.
Now, we can calculate the time it took him for each part of the journey:
Time on paved surfaces = distance / speed = (41 - x) km / 25 km/h
Time off-road = distance / speed = x km / 10 km/h
Since the total time is 2 hours, we can set up an equation:
(41 - x) / 25 + x / 10 = 2
Now, let's solve it!
Don't worry; I won't scare you with complicated math. Clown's honor! 🤡
Multiplying everything by 50 to get rid of those pesky denominators, we have:
2(41 - x) + 5x = 100
Expanding:
82 - 2x + 5x = 100
Combining like terms:
3x = 18
Dividing both sides by 3:
x = 6
Hooray! Kim cycled 6 km off-road on that adventurous day. Now, let's hope he didn't encounter any mischievous, bike-stealing clowns along the way! 🚲🤡
To determine how far Kim cycled off-road, we need to solve the problem step by step.
Step 1: Determine the distance traveled on paved surfaces.
We know that Kim cycled a total of 41 km in 2 hours. This means his average speed was 41 km divided by 2 hours, which equals 20.5 km/h (kilometers per hour). Since we know that Kim cycles at 25 km/h on paved surfaces, we can subtract the off-road portion to determine the distance on paved surfaces.
Distance on paved surfaces = Total distance - Distance off-road
Distance on paved surfaces = 41 km - Distance off-road
Step 2: Determine the time spent on paved surfaces.
We know that to find the distance on paved surfaces, we need to use Kim's average speed of 20.5 km/h. We can use the formula:
Time = Distance / Speed
Time on paved surfaces = Distance on paved surfaces / Speed on paved surfaces
Time on paved surfaces = (41 km - Distance off-road) / 25 km/h
Step 3: Determine the time spent off-road.
We also know that the total time Kim cycled is 2 hours, so the time spent off-road can be found by subtracting the time on paved surfaces.
Time off-road = Total time - Time on paved surfaces
Time off-road = 2 hours - [(41 km - Distance off-road) / 25 km/h]
Step 4: Formulating the equation using time and speed.
Since we have the time spent off-road and the speed off-road, we can now use these values to determine the distance traveled off-road.
Time = Distance / Speed
Time off-road = Distance off-road / Speed off-road
Step 5: Solve the equation.
Now, we can substitute the equation for time off-road from Step 3 into the equation for time off-road from Step 4, and solve for Distance off-road.
[(41 km - Distance off-road) / 25 km/h] = Distance off-road / 10 km/h
To make the equation easier to solve, we can multiply both sides by 25 km/h and 10 km/h to eliminate the denominators:
10 [(41 km - Distance off-road)] = 25 (Distance off-road)
410 km - 10 Distance off-road = 25 Distance off-road
Combining like terms:
410 km = 35 Distance off-road
Finally, solving for Distance off-road:
Distance off-road = 410 km / 35
Distance off-road ≈ 11.71 km
Therefore, Kim cycled approximately 11.71 km off-road.
Two equations, two unknowns.
Let x be the number of offroad km travelled, and y be the number of km on roads.
x + y = 41 (kilometers)
10/x + 25/y = 2 (hours)
Solve for x and y.
10 + 25x/(41-x) = 2x
You end up with a quadratic equation. Take the positive root for x.
If you are not learning algebra yet, you can use a "trial and error" method.
If x = 25 and y = 16, the time spend off roads is 2.5 hours and off raods is 1,6 hours and the totl is 4.1 which is much more than 2 hours.
If x = 5 and y = 36 hours, the time spent off roads is 0.5 hours and the time spent on roads is 1.44 hours, and the totasl is 1.94 hours. You need a bit more time off roads to require 2 hours.
The correct answer wil be 6 km offroad and 35 km on roads.
6/10 + 35/25 = 2.0