Alicia can row 7 miles downstream in the same time it takes her to row 4 miles upstream. She rows downstream 5 miles/hour faster than she rows upstream. Find Alicia’s rowing rate each way.

Question

sriram · Answer

let x be the rate downstream
& y be the speed added by river
x+y= 7/t
x-5-y=4/t
as both 't' r equal

sriram · Answer

stuck here!!

sriram · Answer

7/x+y  =  4 / x-5-y
cross multiply
7x-45-7y=4x+4y
3x-11y=45
x>5  
and x-y-5>0
     x>y+5
i guess we may get more than 1 ans. for this

a_clan · Answer

let speed of boat =Vb
     speed of river =Vr
Given,
     Vr+Vb = 7/t     (1) ----speed of rowing downstream(i.e. speed of boat alongwith river)
     Vr-Vb  = 4/t      (2)----speed of rowing upstream(i.e. speed of boat against  the  flow  of river)

Also given, (Vr+Vb) - (Vr-Vb) = 5 mph
                                      2Vb = 5
                                        Vb = 5/2 mph
Putting back in  eqn (1) and (2), we get
  Vr + 5/2 = 7/t
and Vr - 5/2 = 4/t
On, solving these two equations simultaneously, we get
    t= 3/5 hr

So, rowing downstream rate = 7/t = 35/3 mph
     rowing upstream rate = 4/t = 20/3 mph