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This problem trains for: SAT-I, AMC-8, GMAT, Math Kangaroo 5-6, Math Kangaroo 7-8.

Genghis Khan (around 1200 A.D.), the great Mongol warrior, is credited with the establishment of one of the first systems for relaying mail. Described by the famous Italian traveler Marco Polo, the system had relay stations where a messenger could get a fresh horse. A messenger sent from Bukhara to Samarkand rode through the desert at constant speed of 10 km/h. He stopped at various relays for a total of 1.5 hours. Due to spending time at the relays, his average speed was of only 9.4 km/h. What was the distance he covered that day rounded up to the next kilometer?

Denote the distance between Bukhara and Samarkand by D.

The time spent riding at 10 km/h is:

equation

The total time is:

equation

The average speed is the total distance over total time. Therefore, from the average speed of 9.4 km/h, the total time is also equal to:

equation

Setting the two different expressions for the total time to be equal:

equation

Solve for D:

equation

equation

equation

equation

The distance is 235 km.