Math Help.!!!

[keliao]

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1. A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.

(1)3 km/hr (2)8km/hr(3)4 km/hrANS (4)None of these

 

[UCfan]

Hi Kelio,
I looked at this problem. It is a time consuming problem. However if you know how to handle 4 equations and 4 unknowns, it is not that hard.
Let me explain it you.
Let's right the first 4 equations:
First case
1)(Vman-Vup) t1= 50
2)(Vman+Vup) (9-t1) = 72

Second case
3)(Vman-Vup) t2 = 70
4)(Vman+Vup) (12-t2) = 90

Here is the challenge begin( Very typical engineering analysis problem):
By using 1) I can write
t1= 50/(Vman-Vup)
and putting this into 2) you will get
5)(Vman+Vup) (9- ((50)/(Vman-Vup)))= 72
I am doing same thing for 3) and 4)
and I got
6) (Vman+Vup)(12-((70)/(Vman-Vup)))= 90
By dividing 5) by 6)
u will get
7) (9- ((50)/(Vman-Vup))) / (12-((70)/(Vman-Vup))) = 72/90 = 4/5
Little simplification gives u
45 (Vman-Vup)- 250= 48 (Vman Vup) -280
Finally u will get
8)Vman- Vup= 10
By putting this to 1)
you will get
t1=5 hr
and you can put into 2)
you will get
9)Vman+ Vup = 18
By simultaneously solving
8) and 9)
u will find
Vman = 10 km/hr
Vup= 4 km/hr

I know the solution looks lengthy and hard but solving 4 equations and 4 unknowns takes time by hand( I finished this problem in 1:45 sec) . If I use matlab, it can take only 15 sec . Anyway hopefully it will work.
Regards!