test series

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Feb 20, 2010 12:36 am

It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?

z(y - x)/x + y

z(x - y)/x + y

z(x + y)/y - x

xy(x - y)/x + y

xy(y - x)/x + y

my way of solution was lengthy , suggest some shorter approach
oa will follow soon
source MGMAT test series

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Source: Beat The GMAT — Problem Solving | Sat Feb 20, 2010 12:36 am

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 12:41 am

thephoenix wrote:It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?

z(y - x)/x + y

z(x - y)/x + y

z(x + y)/y - x

xy(x - y)/x + y

xy(y - x)/x + y

my way of solution was lengthy , suggest some shorter approach
oa will follow soon
source MGMAT test series

phoenix please post ur solution too...so that we can think of shorter approach otherwise we might lead in the same direction as you..

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bitsho: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Feb 19, 2010 10:35 pm

by bitsho » Sat Feb 20, 2010 12:50 am

OA is A ?? here is the approach ,which i followed ... assuming distance between town A and town B is 300 miles , the speed of high speed train 100 miles/hr and speed of regular train 50 miles/hrs .

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bitsho: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Fri Feb 19, 2010 10:35 pm

by bitsho » Sat Feb 20, 2010 12:51 am

OA is A ?? here is the approach ,which i followed ... assuming distance between town A and town B is 300 miles , the speed of high speed train 100 miles/hr and speed of regular train 50 miles/hrs .

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vijay_venky: Master | Next Rank: 500 Posts; Posts: 173; Joined: Tue Jul 07, 2009 11:18 pm; Location: Hyderabad; Thanked: 12 times

by vijay_venky » Sat Feb 20, 2010 1:54 am

The velocity of HST=z/x and of NT=z/y

Now because the trains are head-on the relative velocity=z(x+y)/(xy)

Now the time taken for them to meet=z/(relative velocity)=xy/(x+y)

So, in this time the extra distance traveled by HST = time(diff in velocity)=xy/(x+y)[z/x-z/y]

which is z[y-x]/[x+y]

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 8:13 am

thephoenix wrote:It takes the high-speed train x hours to travel the z miles from Town A to Town B at a constant rate, while it takes the regular train y hours to travel the same distance at a constant rate. If the high-speed train leaves Town A for Town B at the same time that the regular train leaves Town B for Town A, how many more miles will the high-speed train have traveled than the regular train when the two trains pass each other?
z(y - x)/x + y
z(x - y)/x + y
z(x + y)/y - x
xy(x - y)/x + y
xy(y - x)/x + y
my way of solution was lengthy , suggest some shorter approach
oa will follow soon
source MGMAT test series

Just go like this let p be distance covered by HST and z-p by RT when they cross each other so their time taken is equal
--> p/(z/x)= (z-p)/((z/y) --> px = yz-py --> p=yz/(x+y)
so extra distance covered = p-(z-p) = 2p-z = 2yz/(x+y) -z = [spoiler]z(y-x)/(x+y) Ans A[/spoiler]

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