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:

1. Original time to reach the place = 40 hours
2. 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.
3. 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:

1. D = 40S
2. 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.