MonSama wrote:
Mischa drove from A to B, a distance of 100 miles, at an average speed of 50 miles per hour, and then back from B to A along the same route at an average speed of m miles per hour. What is the value of m?
(1) Mischa’s average speed for the entire round trip, excluding any time he spent at point B, was \(\frac{m+50}{2}\) miles per hour.
(2) If Mischa’s average speed from B to A had been 20% slower, the total time for the entire round trip, excluding any time Mischa spent at point B, would have been 12.5% greater.
You actually don't need to get to the absolute value of m (as this is not PS :p )
Average speed = Total Distance/Total time.
(1) Let time take to travel from B to A be t hours.
=> t = 100/m -- (A)
by FS 1 - 200/(t+2) = (m+50)/2
we have already derived a relation between t and m in (A)
so m can easily be worked out (i did not solve the quadratic)
(2) if the avg speed from B to A would be have been 20% lesser i.e. avg speed shall be 0.8m
so it took 12.5% extra time for the entire round trip because of this change in speed
Let original time taken for the round tripe be T.
T = 200/(t+2)
now when m becomes 0.8m, T becomes 1.125T.
in this case also we have a relation between T and t, t and m. so m can be worked out.
Answer, therefore, should be D.
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