A boy walked for 4 hours and cycled for 3 hours,covering a total distance of 74 kilometers,later he walked for 2 hours and cycled for 4 hours ,covering 82 kilometers,what were his average speed of walking and his average speed of cycling if his speed was constant in the two cases?
4w+3c = 74
2w+4c = 82
c=18, w=5
if the speed was constant, there's no need to talk about an average speed. However, in real life such speeds are never constant, so they should have just asked about the average speed.
To find the average speed of walking and cycling, we need to calculate the total distances traveled in each mode of transport and divide them by the corresponding total time taken.
Let's start with the first case:
The boy walked for 4 hours and cycled for 3 hours, covering a total distance of 74 kilometers.
To find the distance he walked, we subtract the distance covered while cycling from the total distance:
Distance walked = Total distance - Distance cycled
Distance walked = 74 km - Distance cycled
Now, we know the time he spent walking (4 hours) and we want to find the distance walked in kilometers:
Average speed of walking = Distance walked / Time spent walking
Using the same logic, we can find the distance he cycled:
Average speed of cycling = Distance cycled / Time spent cycling
Let's move to the second case:
The boy walked for 2 hours and cycled for 4 hours, covering a total distance of 82 kilometers.
In this case, we again find the distance walked and the distance cycled using the same approach as in the first case.
Average speed of walking = Distance walked / Time spent walking
Average speed of cycling = Distance cycled / Time spent cycling
Now, we have all the necessary information to calculate the average speed.
Average speed of walking in the first case = Distance walked in the first case / 4
Average speed of walking in the second case = Distance walked in the second case / 2
Average speed of cycling in the first case = Distance cycled in the first case / 3
Average speed of cycling in the second case = Distance cycled in the second case / 4
To obtain the average speed of walking and cycling, we can calculate the average of the speeds from the two cases:
Average speed of walking = (Average speed in the first case + Average speed in the second case) / 2
Average speed of cycling = (Average speed in the first case + Average speed in the second case) / 2
Solving these equations will give us the average speeds of walking and cycling.