Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

the last of the identities, quadratics and partial fractions response

Here are the final questions I just cannot get at all, I've tried so many times but have had no success whatsoever.

Here is the first question:

Two trains are travelling at uniform speeds. The slower train takes a hours longer to cover b km. It travels 1km less than the faster one in c hours.
a) What is the speed of the faster train in terms of a,b and c.
b) if a, b and c, and the speeds of the trains, are rational numbers, find five sets of values for a,b and c. Choose and discuss two sensible sets of values.

Here is the second question:

A tank can be filled using two pipes. The smaller pipe alone will take a minutes longer than the larger pipe alone to fill the tank. Also the smaller pipe will take b minutes longer to fill the tank then when both pipes are used.
a) Find, in terms of a and b, how long it will take each of the pipes to fill the tank.
b) If a = 24 and b = 32, find how long it takes for each of the pipes to fill the tank.
c) If a and b are consecutive positive integers, find five pairs of values of a and b such that b^2-ab is a perfect square. Interpret these results in the context of this tank problem.

I would be so grateful for any help at all, I really am stuck.
Thanks greatly in advance,
Glenn.

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"If your going through hell, keep going."

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: the last of the identities, quadratics and partial fractions response

1(a)
Suppose the speed of the faster train is v.

Then it can travel b km in b⁄v hours.

The slower train takes a+b⁄v hours to travel b km; so its speed is

km per hour.

So in c hours the slower train travels

km while the faster one travels cv km.

Set

and solve for v in terms of a, b, c.

2(a)
Suppose the larger pipe takes t minutes to fill the tank.

Then in 1 minute it can fill 1⁄t of the tank.

So in 1 minute the smaller pipe can fill 1⁄(t+a) of the tank.

If both pipes are on, 1⁄t + 1⁄(t+a) of the tank can be filled in 1 minute.

So the time taken for tank to be filled with both pipes on is

minutes.

Set

and solve for t in terms of a and b.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: the last of the identities, quadratics and partial fractions response

Thank you Jane,
you described them exactly as I wanted, thank you so much:D

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"If your going through hell, keep going."