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#1 2015-10-02 01:24:16

FiST2015
Member
Registered: 2015-10-02
Posts: 1

My brother needs help and asked me! (Step by step explanation needed)

Person A left Town X at 10:18 am. He walked at a constant speed and arrived at town Z at 1:30 pm. On the same day, Person B left town Z at 9 am. Person B walked the same route in the opposite direction at a constant speed. Person B arrived at town X at 11:40 am. The road crosses a wide river. By coincidence, both arrived at the bridge on opposite sides of the river at the same instant. Person A left the bridge 1 minute later than Person B. At what time did they arrive at the bridge?

Thanks for all the help! smile

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#2 2015-10-02 06:35:22

Bob
Administrator
Registered: 2010-06-20
Posts: 10,052

Re: My brother needs help and asked me! (Step by step explanation needed)

hi FiST2015

Welcome to the forum.

The idea for solving this sort of problem is simple enough, but the times in this problem make the arithmetic especially complicated.  Yuck!  I leave that bit to you and your brother.

Start with a distance time graph to show A and B's journeys.  I took me 4 goes before I had a decent graph.  This is NOT to scale.  It just represents what is going on.

The two towns are shown on the up axis.  Times are shown across.  I have converted all times into minutes from 9.00am.

NjZ90XN.gif

The two horizontal lines across the middle represent the near and far side of the river bridge.

If I call the distance between the towns, D, and the speeds V_subscript_a and V_subscript_b, then using distance = speed x time

From this you can get the ratio of the speeds.

Now suppose the bridge has length L and t_sub_a, and t_sub-b are the times to cross:

We also know that

Using these equations you can calculate both times to cross in minutes.

Now call the time at which both arrive at their side of the bridge, t.

For A, calculate the distance he has travelled at this time in terms of his speed and t.

For B, calculate the same distance by finding the time he leaves the bridge (t + t_sub_b), computing his remaining journey time and using his speed.

Equate these distances, substitute in the ratio of the speeds and you are left with an equation in t.  Solve for the answer to the question.

Best of luck smile

Bob

ps.  Made a silly mistake with my arithmetic.  It's not as bad as I thought and t comes out to be a 'nice' time.

Last edited by Bob (2015-10-02 07:20:16)


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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