方程式!!!

1.Tom has $342 and Tim has $186. How much must Tom give to Tim so that
Tim may have three times as much as Tom?
Let Tom give x dollars to Tim
Such that
3(342 – x) = 186 + x
1026 – 3x = 186 + x
4x = 840
x = $210

2.A train starts at 8a.m. and travels at the rate of 60km per hour.At 12 noon a
helicopter sets out from the same place to overtake it, travelling at the rate of
150km an hour. Where will it overtake the train?
Let helicopter overtake the train will at x km
Such that
x / 60 = x/150 + 4
5x = 2x + 1200
3x = 1200
x = 400km

3.Divide $94 between A, B and C, so that B may have $37 more than A, and C's share may be $13 more than twice A's share. How much does A's share? How much does B's share? How much does C's share?
Let A have x dollars
B have x + 37
C have 2x + 13
Such that
x + (x + 37) + (2x + 13) = 94
x + x + 37 + 2x + 13 = 94
4x = 44
x = 11
So A have $11
B have 11 + 37 = $48
and C have 2*11+13 = $35

1.

3(342 – x) = 186 + x

1026 – 3x = 186 + x

4x = 840

x = $210



2.

x / 60 = x/150 + 4

5x = 2x + 1200

3x = 1200

x = 400km

B have x + 37

C have 2x + 13



3.

x + (x + 37) + (2x + 13) = 94

x + x + 37 + 2x + 13 = 94

4x = 44

x = 11

So A have $11

B have 11 + 37 = $48

and C have 2*11+13 = $35

It is easy.

1. Let $X be the amount that Tom has to give to Tim so that Tim will have three times as much as Tom has.

Then, 3(342-X)=186+X
1026 -3X = 186 +X
1026 -186 = X + 3X
840 = 4X
X = 210

(checking : if Tom gives Tim $210, Tom will have $132 left behind and Tim will have $396, which is exactly three times of $132)

The amount required to be found is $210.

2. At 12:00 noon, the train is 240 km (i.e. 60km per hour x 4 hours) away from the starting point. Let Y hours after 12:00 noon be the time when the helicopter will overtake the train. The train will by then be 240 + 60Y away from the starting point. And the helicopter will be 150Y away from the starting point, so we have:

150Y = 240 + 60Y
90Y = 240
Y = 2 2/3

So, the helicopter will overtake the train at 2:40 p.m.