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This problem trains for: SAT-I, GMAT, AMC-8, AMC-10, Math Kangaroo 5-6, Math Kangaroo 7-8.

Honoria types 60% more characters per minute than Wilmott and 60% less characters per minute than Bertie. If the difference between the largest and the smallest typing rates of these three characters is 15 characters per minute, find the median typing rate in characters per minute.

(characters from P.G. Wodehouse)

Let us denote Honoria's rate by h, Bertie's by b and Wilmott's by w. Then, Honoria's rate is equal to 160% of Wilmott's rate and 40% of Bertie's rate.

equation

equation

Therefore,

equation

equation

And the difference between the slowest (Wilmott) and the fastest (Bertie) is:15 characters per minute:

equation

Solving for h:

equation

equation

equation

we obtain Honoria's typing rate, which is also the median rate, for obvious reasons. (She types faster than Wilmott but slower than Bertie.)