# Find the Distance between Aplha and Gamma

Maharshi walks from Alpha to Gamma in four days, and back in five days. Each day he walks 1km less than on the preceding day. What is the distance between Alpha and Gamma?

Answer: Distance between Alpha and Gamma is 90 km

Explanation

Maharshi walks from Alpha to Gamma in 4 days.

Let us assume he walks x km in first day

(x-1) km in second day

(x-2) km in third day

(x-3) km in fourth day

Let total distance between Alpha and Gamma be d.

d = x + (x-1) + (x-2) + (x-3)

d = 4x - 6

Now, Gamma to Alpha which which Maharshi finishes in 5 days.

(x-4) km in first day

(x-5) km in second day

(x-6) km in third day

(x-7) km in fourth day

(x-8) km in fifth day

Total distance between Gamma and Alpha

d = (x-4) + (x-5) + (x-6) + (x-7) + (x-8)

so d = 5x - 30

As distance between Aplha and Gamma is same as distance between Gamma and Alpha

4x - 6 = 5x - 30

x = 24

Substituting the value of x in equation d = 4x - 6

d = 4(24) - 6

d = 90 km

Explanation

Maharshi walks from Alpha to Gamma in 4 days.

Let us assume he walks x km in first day

(x-1) km in second day

(x-2) km in third day

(x-3) km in fourth day

Let total distance between Alpha and Gamma be d.

d = x + (x-1) + (x-2) + (x-3)

d = 4x - 6

Now, Gamma to Alpha which which Maharshi finishes in 5 days.

(x-4) km in first day

(x-5) km in second day

(x-6) km in third day

(x-7) km in fourth day

(x-8) km in fifth day

Total distance between Gamma and Alpha

d = (x-4) + (x-5) + (x-6) + (x-7) + (x-8)

so d = 5x - 30

As distance between Aplha and Gamma is same as distance between Gamma and Alpha

4x - 6 = 5x - 30

x = 24

Substituting the value of x in equation d = 4x - 6

d = 4(24) - 6

d = 90 km