A man can reach a certain place in 40 hours. If he reduces his speed by 1/15th, he goes 5km less in that time. Find the total distance covered by him.
Let's call the original speed of the man "S" (in km/h) and the total distance he needs to cover "D" (in km).
According to the given information:
- Original time to reach the place = 40 hours
- Reduced speed is 1/15 less than the original speed, so the reduced speed is (S - S/15) km/h, which simplifies to (14S/15) km/h.
- When he reduces his speed, he goes 5 km less in the same time.
So, we can set up the equation using the formula:
Distance = Speed × Time
For the original speed: D = S × 40
For the reduced speed: D - 5 = (14S/15) × 40
Now, we have two equations:
- D = 40S
- D - 5 = (14S/15) × 40
We can solve this system of equations to find the values of D and S. First, we'll solve equation (2) for D:
D - 5 = (14S/15) × 40 D = (14S/15) × 40 + 5
Now, we'll substitute this expression for D into equation (1):
(14S/15) × 40 + 5 = 40S
Let's solve for S:
(14S/15) × 40 + 5 = 40S
Multiply both sides by 15 to eliminate the fractions:
14S × 40 + 5 × 15 = 40S × 15
Now, simplify:
14S × 40 + 75 = 600S
Subtract 14S × 40 from both sides:
75 = 600S - 560S
Combine like terms:
75 = 40S
Now, divide both sides by 40 to find the value of S:
S = 75 / 40 S = 1.875 km/h
Now that we have the original speed (S), we can find the total distance (D) using equation (1):
D = 40S D = 40 × 1.875 D = 75 km
So, the total distance covered by the man is 75 km.
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