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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 7-8, Math Kangaroo 9-10.

While the regiment marches away from Lucknow at a speed of 2.5 miles per hour, Gunga Din distributes water to soldiers from the front of the 0.25 mile long column to the back. Then, he returns to the front to wait for another water supply point. While distributing water, Gunga Din walks forward at a speed of 1 mile per hour but after giving away the water he runs towards the front of the column at a speed of 4 miles per hour. How many minutes did it take Din to distribute the water and return to his post?

(characters from Rudyard Kipling's poem "Gunga Din")

Divide the distance (length of column) by the speed to find the time it takes Din to distribute the water. Din's speed in mph during this is:

equation

and the time used is:

equation

On the way back to the front Din walks at a speed of:

equation

with respect to the column. Therefore, he reaches the front after a time equal to:

equation

The total time it takes Din to distribute water to the troop is:

equation