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# Mike and Sue are running toward each other. The ratio

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Mike and Sue are running toward each other. The ratio [#permalink]  18 Oct 2006, 01:16
3. Mike and Sue are running toward each other. The ratio between Mikeâ€™s speed and Sue's speed is 4 to 7 and the distance between them is 352 meters. What is the distance Sue passed?

(A) 96m (B) 128m (C) 222m (D) 224m (E) 312m
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Re: Rate and Ratio Combo Question. [#permalink]  18 Oct 2006, 02:47
ishtmeet wrote:
3. Mike and Sue are running toward each other. The ratio between Mikeâ€™s speed and Sue's speed is 4 to 7 and the distance between them is 352 meters. What is the distance Sue passed?

(A) 96m (B) 128m (C) 222m (D) 224m (E) 312m

What this question is asking for? Is it written this way originally?

Last edited by SimaQ on 18 Oct 2006, 03:02, edited 1 time in total.
Director
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[#permalink]  18 Oct 2006, 02:56
I suppose it asks for number of meters Sue has covered when she met Mike...

I would pick B....

I am sure there are some shortcurts to solving this, but i take the definite way my approach took me around 2 min....
Senior Manager
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[#permalink]  18 Oct 2006, 04:46
My answer is D. What is the OA?
Director
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[#permalink]  18 Oct 2006, 05:18
Yes D.... I did not complete my calculations.... that is, 352-128=224... have to stop rushing things....
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[#permalink]  18 Oct 2006, 05:30
My solving:

Creating the table

Sue: rate= 7/1, time=t, distance=d
Mike: rate= 4/1, time=t, distance=352-d

Make two eqation:

7/1t=d
4/1t=352-d.....replace d with 7/1t

4/1t=352-7/1t
4/1t+7/1t=352
11/1t=352
t=32

To know what distance Sue has covered when she met Mike simply use r*t=d formula.

7/1*32=d
d=224.
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[#permalink]  18 Oct 2006, 22:36
Time = Distance/speed

They would hav spent same amount of time when they meet,
lets say mike ran x m and sue ran 352-x m, let m and be their respective speeds

so

x/m = (352-x)/s

x/(352-x) = m/s

x/(352-x) = 4/7 (putting the speed ratio)

x = 128

352-128 = 224

D
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[#permalink]  19 Oct 2006, 03:28
Should be B.

Total relative speed is 11 units. She would have covered
4*352/11 = 128 m
Director
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[#permalink]  19 Oct 2006, 03:30
Didn't rewrite the question, as I should have done. It is
7*352/11 = 224

D is the correct answer.
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[#permalink]  19 Oct 2006, 08:38
Yes (D) ..since their speed ratios are 4:7 hence Sue covers 7*(352)/11=224
[#permalink] 19 Oct 2006, 08:38
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# Mike and Sue are running toward each other. The ratio

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