SOLUTION: x takes 3 hrs more than y to walk 30 km. but if x doubles his pace he is ahead of y by 1 1/2 hours.find their speed of walking

Algebra ->  Linear-equations -> SOLUTION: x takes 3 hrs more than y to walk 30 km. but if x doubles his pace he is ahead of y by 1 1/2 hours.find their speed of walking      Log On


   

Question 1164936: x takes 3 hrs more than y to walk 30 km. but if x doubles his pace he is ahead of y by 1 1/2 hours.find their speed of walking
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
               SPEED        TIME        DISTANCE

x             30/(t+3)      t+3          30

y             30/t          t            30

-------------------------------------------------

x           60/(t+3)     (t+3)/2        30

y           30/t          t             30

difference              (3/2)

t-%28t%2B3%29%2F2=3%2F2
-
Solving that equation gives highlight_green%28t=6%29

Speed for x, 30%2F%286%2B3%29=30%2F9=10%2F3=highlight%283%261%2F3%29k%2Fhour
Speed for y, highlight%285%29k%2Fhour


-
A different opinion or approach may be good.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

x takes 3 hrs more than y to walk 30 km. but if x doubles his pace he is ahead of y by 1 1/2 hours.find their speed of walking
It may be easier to find the time 1st, but I always like to ZERO IN right away on the answers that're needed.

Let x's and y's speeds be x and y, respectively

We then get the following TIME equation: matrix%282%2C3%2C+3%2C+%22=%22%2C+30%2Fx+-+30%2Fy%2C+1%2C+%22=%22%2C+10%2Fx+-+10%2Fy%29

                                         xy = 10y - 10x ------ eq (i)

                            We also get: 

                                         xy = - 10y + 20x ------ eq (ii)

                                         2xy = 10x ------ Adding eqs (i) & (ii)

                                         y's speed, or 

                           x(5) = 10(5) - 10x ------ Substituting 5 for y in eq (i)

                           5x = 50 - 10x

                           5x + 10x = 50

                           15x = 50

                           x's speed, or