Bunuel
While driving from Corvallis to Portland, Matt obeys the speed limit. Matt’s friend Vadim likes to drive faster than the speed limit and believes that he could leave well after Matt and still reach Portland first. The distance from Corvallis to Portland is 81 miles and both Matt and Vadim travel the same route at their respective constant speeds. If Matt travels at a constant speed of 36 mph and leaves 90 minutes before Vadim, what is the minimum constant speed that Vadim must exceed in order to arrive in Portland before Matt?
A. 72 mph
B. 81 mph
C. 96 mph
D. 108 mph
E. 162 mph
Kudos for a correct solution.
Speed of Matt = 36 mph
Speed of Vadiim = v
Now Matt Leaves 90 minutes before vadim. So, during this time Matt travels 36*90/60 = 54 Miles
The distance left to reach Portland = 81 - 54 = 27 miles
At this time Vadim starts travelling and he has to travel atleast 81 miles during the time Matt travels next 27 miles
So,
27/81 = 36/v
-> v = 108
So if vadim has a speed just greater than 108 he will reach before matt....
So, vadim must exceed 108 mph in order to arrive in Portland before Matt
Answer D