Jim begins a trip by driving for y hours at a constant speed of 65 miles per hour, and then slows to a constant speed of 55 miles per hour for the rest of the trip. What is the total distance Jim drives, in miles, if the trip takes x hours, and x > y?

\(a) \frac{65 + 55}{x-y}\)
\(b) \frac{65y + 55x}{x-y}\)
\(c) \frac{65}{y} + \frac{55}{x}\)
d) 65(y–x)+ 55(x–y)
\(e) 10y + 55x\)

IMO E.

I actually solved this one using POE. It took me 10 seconds, but I would still prefer Bunuel approach . Not sure if many ppl will like it but in case we are pressed for time, we could try this approach.

A. 65+55/(x-y) => (mi/hr) / hr will not give you distance in miles any how.
B. 65y+55x/(x-y) => (mi/hr) will not give you distance in miles
C. (65/y) + (55/x) => Same as A

Now we have only 2 options D & E. We already know that (x>y) , therefore y-x<0. This implies that 65(y-x)+55(x-y) <0 and distance can never be less than 0 as we consider it as an absolute quantity here.

Left is option E which looks reasonable and hence IMO E.

Hope this helps!!

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