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Pat traveled a distance of 240 miles in x hours. For a part

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Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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New post 22 Jun 2013, 00:04
1
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A
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D
E

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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
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Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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New post 22 Jun 2013, 09:06
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.
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Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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New post 22 Jun 2013, 09:58
3
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.

Answer: E.
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Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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New post 30 Jul 2013, 11:56
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?
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Re: Pat traveled a distance of 240 miles in x hours. For a part  [#permalink]

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New post 22 Jul 2014, 02:50
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.
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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, 07:53
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