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Director  Joined: 29 Nov 2012
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Jim begins a trip by driving for y hours at a constant speed  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 77% (02:00) correct 23% (02:28) wrong based on 233 sessions

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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)
$$e) 10y + 55x$$
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Joined: 02 Sep 2009
Posts: 58381
Re: Jim begins a trip by driving for y hours at a constant speed  [#permalink]

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fozzzy wrote:
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)
$$e) 10y + 55x$$

The distance covered at 65 miles per hour = (rate)*(time) = 65y miles.
The distance covered at 55 miles per hour = (rate)*(time) = 55(x-y) miles.

65y + 55(x-y) = 10y + 55x miles.

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Re: Jim begins a trip by driving for y hours at a constant speed  [#permalink]

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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!! SVP  B
Joined: 06 Nov 2014
Posts: 1873
Re: Jim begins a trip by driving for y hours at a constant speed  [#permalink]

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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?

*distance = speed * time
speed 1 = 65 / speed 2 = 55 / time 1 = y / time 2 = x - y

distance = (65 * y) + (55 * (x-y)) = (65y) + (55x-55y) = 10y+55x
a)65+55x−y
b)65y+55xx−y
c)65y+55x
d) 65(y–x)+ 55(x–y)
e)10y+55x
Non-Human User Joined: 09 Sep 2013
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Re: Jim begins a trip by driving for y hours at a constant speed  [#permalink]

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_________________ Re: Jim begins a trip by driving for y hours at a constant speed   [#permalink] 02 Feb 2019, 02:57
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