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On his trip from Alba to Benton, Julio drove the first x [#permalink]

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20 Dec 2005, 08:57

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On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first X miles?

(1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles (2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance

How do you guys calculate for how many miles he drove 50 miles/hour and for how many miles he drove 60 miles an hour?

Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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20 Dec 2005, 10:55

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sandalphon wrote:

On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 milesper hour. How long did it take Julio to drive the first x miles?

(a) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.

How do you guys calculate for how many miles he drove 50 miles/hour and for ho wmany miles he drove 60 miles an hour?

I'm assuming this is a PS question...
rt=D

I would set it up like this; we will call the 2 segments of the trip A, and B.

....... A ........ B R ..... 50 ...... 60

T ...... t ....... 10-t

D ....... x ....... 530-x

Derive 2 equations from this.

50t = x
60(10-t) = 530-x

Substitute

600 - 60t = 530 - 50t
Solve for t, you get t = 7... Answer is 7 hours

Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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08 Jun 2010, 10:07

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sandalphon wrote:

On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 milesper hour. How long did it take Julio to drive the first x miles?

(a) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.

How do you guys calculate for how many miles he drove 50 miles/hour and for ho wmany miles he drove 60 miles an hour?

the complete question is..

On his trip from Alba to Benton, Julia drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first x miles ? 1) On his trip, Julio drove for a total of 10 hrs and drove a total of 530 miles 2) On his trip,it took Julio 4 more hours to drive the first x miles than to drive the remaining distance.

Solution: d=vt

let d=total distance t1=total time taken to cover x miles t2=total time taken to cover d-x miles (the remaining miles)

t1=x/50 ; t2=(d-x)/60 ----> we have these equations before even looking at the statemenets

statement(1) t1+t2=10; d=530 put the values in the above equations

x/50 + (530-x)/60 = 10

no need to calculate x's value. just looking at the equation, we can see that x's value can be determined and, thus, the value of t1 can be determined.

SUFFICIENT

statement(2) t1=t2+4 we still don't know the value of d, so we can't calculate the value of t1.

INSUFFICIENT

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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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15 May 2011, 20:37

Lets solve this by alligation.

From Statment 1: Avg speed=53 mile/hr it comes from avg of 2 speeds 50 and 60 (as per Q) 50--53------60 53 is closer to 50 hence we need travel more at 50 miles/hr speed. Total hours 10 need to divided in to speeds 50 and 60. Time spend will be in inverse ration of two speeds 50--53------60 7hrs--------3 hrs

@shantascherla: how can you assume numbers when they are given in the question.

Well but i think it will work if you are solving DS question and you are aware that you dont need to find the correct answer. All you got to do is find out if a Unique ans is possible or not.
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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27 Feb 2016, 17:40

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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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22 Nov 2016, 08:50

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sandalphon wrote:

On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first X miles?

(1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles (2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance

How do you guys calculate for how many miles he drove 50 miles/hour and for how many miles he drove 60 miles an hour?

the answer is A. i created two expressions time traveled first x miles: x/50 time traveled remaining part: D-x/60, where D is the total distance.

1. D = 530, and we can write: x/50 + 530-x/60 = 10 -> we can solve for X, we can find x/50 - sufficient.

2. x/50 - D-x/60 = 4 -> we still have 2 unknowns, we can't answer the question - not sufficient.