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problem with speed difficult

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Taniuca: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Aug 02, 2010 3:25 pm; Thanked: 3 times

by Taniuca » Mon Nov 01, 2010 5:10 pm

Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z?

a) 81
b) 90
c) 105
d) 125
e) 150

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Source: Beat The GMAT — Problem Solving | Mon Nov 01, 2010 5:10 pm

pesfunk: Master | Next Rank: 500 Posts; Posts: 286; Joined: Tue Sep 21, 2010 5:36 pmFollowed by: 5 members; Location: Kolkata, India; Thanked: 11 times

by pesfunk » Mon Nov 01, 2010 5:40 pm

After z minutes, Car Y travelled 54*z miles
Till then, Car X had travelled for 18+z minutes

so distance travelled by X = 40 (18 + z )

As per question: 54 * z - 40 ( 18 + z ) = 23

or 54z - 720 - 40z = 23

or 14Z = 743

or z = 53

Where am I going wrong ?

Taniuca wrote:Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z?

a) 81
b) 90
c) 105
d) 125
e) 150

Like this post

pesfunk: Master | Next Rank: 500 Posts; Posts: 286; Joined: Tue Sep 21, 2010 5:36 pmFollowed by: 5 members; Location: Kolkata, India; Thanked: 11 times

by pesfunk » Mon Nov 01, 2010 5:46 pm

OK. Missed that the speed was in hours

so 23 has to be multiplied by 60

correct equation => 54 * z - 40 ( 18 + z ) = 23*60

or Z = 150

pesfunk wrote:After z minutes, Car Y travelled 54*z miles
Till then, Car X had travelled for 18+z minutes

so distance travelled by X = 40 (18 + z )

As per question: 54 * z - 40 ( 18 + z ) = 23

or 54z - 720 - 40z = 23

or 14Z = 743

or z = 53

Where am I going wrong ?

Taniuca wrote:Car X left Town T traveling at an average speed of 40 miles per hour. Car Y left Town T 18 minutes after car X left Town T, and car Y traveled at an average speed of 54 miles per hour. When car Y had traveled for z minutes, car Y had traveled 23 miles more that car X had from the time that car X left Town T. What is the value of z?

a) 81
b) 90
c) 105
d) 125
e) 150

Like this post

Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pmFollowed by: 164 members; Location: Toronto; Thanked: 539 times; GMAT Score:800

by Testluv » Mon Nov 01, 2010 5:51 pm

Hi,

This is a catch-up problem in which the slower moving object has a headstart on the faster moving one. Car x travels for 18 minutes before Car y moves at all. In this 18 minutes, Car x gains a headstart of 12 miles (since it's travelling at 40mph).

When two objects are travelling in the same direction, we can subtract their rates. That is, Car y will "catch-up" or close this 12 mile headstart at a rate of 54-40 = 14 mph. Once Car y catches up to car x, it will then exceed car x at this same rate. We know that Car y needs to catch up 12 miles, and then exceed Car x for another 23 miles. So, that's a total of 35 miles. The rate of catch-up/excess is 14. So, z or the time of all of this is 35/14 or 2.5 hours or 150 minutes.

Choose E.

Kaplan Teacher in Toronto

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