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Intern  Joined: 13 May 2013
Posts: 20
Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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5 00:00

Difficulty:   55% (hard)

Question Stats: 68% (02:47) correct 32% (01:58) wrong based on 176 sessions

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Pat traveled a distance of 240 miles in x hours. For a part of journey he was travelling at constant speed of 40 miles per hour whereas for the remaining part of the journey he was traveling at constant speed of z miles per hour. How long was he traveling at z miles per hour.

(1) Average speed for the journey is 48 miles per hour.
(2) z > 48 miles per hour
Senior Manager  Joined: 28 Dec 2010
Posts: 261
Location: India
Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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got the right answer.. but in almost 5 mins! My approach was to make an RTD chart. i.e
R T D
40 t 40t
Z x-t Z(x-t)
x 240

thus 40t + Z(x-t) = 240

Now statement 1 just gives x in the equation i.e 5 hrs. We still need either of Z or t to get a linear equation.
Statement 2 alone says nothing about x or t.

combined says x= 5 hrs z>48 but Z can be any value higher than 48. As z increases the time of travel at z speed will reduce while at 40 miles/hr will increase to make the total time of travel equal to 5 hrs. Hence insufficient.
Math Expert V
Joined: 02 Sep 2009
Posts: 58396
Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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Pat traveled a distance of 240 miles in x hours. For a part of journey he was travelling at constant speed of 40 miles per hour whereas for the remaining part of the journey he was traveling at constant speed of z miles per hour. How long was he traveling at z miles per hour.

(1) Average speed for the journey is 48 miles per hour. (Total time)=(Total distance)/(Average Speed), thus this statement implies that (Total time)=x=240/48=5 hours. So, we have that zt+40(5-t)=240 --> zt+200-40t=240 --> t(z-40)=40. Not sufficient.

(2) z > 48 miles per hour. Clearly insufficient.

(1)+(2) We have that t(z-40)=40 and z>48. Still insufficient to get t.

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Senior Manager  Joined: 13 May 2013
Posts: 398
Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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Pat traveled a distance of 240 miles in x hours. For a part of the journey he was traveling at constant speed of 40 miles per hour whereas for the remaining part of the journey he was traveling at constant speed of z miles per hour. How long was he traveling at z miles per hour.

(1) Average speed for the journey is 48 miles per hour.

Speed = Distance/Time
48 = 240/T
T = 5
Pat was on the road for five hours.

There are two parts to the journey - part one at 40 miles/hour and part two at z miles/hour

t1 + t2 = total
(d/40) + (240-d)/z = 5
(d/40) + (240/zd) = 5
d^2z/40dz + 9600/40dz = 5
(d^2z + 9600) / 40dz = 5
d^2z + 9600 = 200dz
d^2z - 200dz + 9600 = 0
I am left with (d) and (z)
INSUFFICIENT

Is this a correct way of solving the problem?
Manager  Joined: 21 Oct 2013
Posts: 178
Location: Germany
GMAT 1: 660 Q45 V36 GPA: 3.51
Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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Instead of calculating, would it be possible to say that both stmts are IS because neither gives you the exact time or distance traveled for one of the parts of the trip? If I look at your calculations (which I also did) it comes down to this problem for me.
Non-Human User Joined: 09 Sep 2013
Posts: 13382
Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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_________________ Re: Pat traveled a distance of 240 miles in x hours. For a part   [#permalink] 21 Oct 2018, 08:53
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