A man travels to work everyday at a speed of 40km/h using a car and 6km/h by walking. He arrives at his workshop in 25mins. One day his car broke down and he walked three times as far, thereby arriving at the workshop 17mins late. Calculate the distance from his house to the workshop
distance by car -- x
distance walking -- y
x/40 + y/6 = 25/60
times 120
3x + 20y = 50
on breakdown:
distance walking = 3y
distance by car = (x+y) - 3y = x - 2y
3y/6 + (x-2y)/40 = 42/60
times 120 again
60y + 3x - 6y = 84
3x + 54y = 84
subtract the two equations,
34y = 34
y = 1 km
x = 10 by subbing in the 1st equation.
so the distance is 11 km
To solve this problem, we need to find the distance from his house to the workshop.
Let's assume the distance from his house to the workshop is "d" kilometers.
When he travels by car at a speed of 40 km/h, he takes 25 minutes to reach the workshop. This can be converted to hours by dividing by 60: 25/60 = 0.417 hours.
So, when he travels by car:
Time taken = Distance / Speed
0.417 = d / 40
d = 0.417 * 40
d = 16.68 km
Now, let's consider the situation when his car broke down and he walked three times the distance. This means he walked 3 * 16.68 km = 50.04 km.
In this case, he arrives at the workshop 17 minutes late. So, the total time taken when he walks is 25 + 17 = 42 minutes.
Again, converting to hours: 42/60 = 0.7 hours.
Utilizing the walking speed of 6 km/h, we can calculate the distance using the formula:
Time taken = Distance / Speed
0.7 = 50.04 / 6
50.04 = 0.7 * 6
50.04 = 4.2 km
Therefore, the distance from his house to the workshop is approximately 4.2 km when his car is broken, and it is around 16.68 km when he travels by car.