SOLUTION: one day Manisha covered a distance of 24 KM at x km/hr and another 40Km at Y km/hr.Next day,she covered 18km at X Km/hr and another 48Km at y km/hr if each day she took 9 hrs to co

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Question 1065246: one day Manisha covered a distance of 24 KM at x km/hr and another 40Km at Y km/hr.Next day,she covered 18km at X Km/hr and another 48Km at y km/hr if each day she took 9 hrs to complete the journey. Find the values of X & Y.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think I will end up with 4 equations and 4 unknowns,
which means it is solvable
-------------------------
For the 1st day:
Let the time for the 24 km trip be +t%5B1%5D+ hrs
The time for the 40 km trip is +9+-+t%5B1%5D+ hrs
For the 2nd day:
Let the time for the 18 km trip be +t%5B2%5D+ hrs
The time for the 48 km trip is +9+-+t%5B2%5D+ hrs
--------------------------------------------
That gives me the 4 unknowns:
+x+, +y+, +t%5B1%5D, and +t%5B2%5D+
--------------------------------------
(1 ) +24+=+x%2At%5B1%5D+
(2) +40+=+y%2A%28+9+-+t%5B1%5D+%29+
(3) +18+=+x%2At%5B2%5D+
(4) +48+=+y%2A%28+9+-+t%5B2%5D+%29+
-------------------------------
(2) +y+=+40%2F%28+9+-+t%5B1%5D+%29+
Substitute this into (4)
(4) +48+=+%28+40%2F%28+9+-+t%5B1%5D+%29+%29%2A%28+9+-+t%5B2%5D+%29+
(4) +48%2A%28+9+-+t%5B1%5D+%29+=+40%2A%28+9+-+t%5B2%5D+%29+
(4) +6%2A%28+9+-+t%5B1%5D+%29+=+5%2A%28+9+-+t%5B2%5D+%29+
(4) +54+-+6t%5B1%5D+=+45+-+5t%5B2%5D+
(4) +6t%5B1%5D+-+5t%5B2%5D+=+9+
and
(1) +x+=+24%2Ft%5B1%5D+
Substitute into (3)
(3) +18+=+%28+24%2Ft%5B1%5D+%29%2At%5B2%5D+
(3) +18t%5B1%5D+=+24t%5B2%5D+
(3) +3t%5B1%5D+=+4t%5B2%5D+
(3) +t%5B2%5D+=+%283%2F4%29%2At%5B1%5D+
---------------------------
Substitute (3) into (4)
(4) +6t%5B1%5D+-+5%2A%283%2F4%29%2At%5B1%5D+=+9+
(4) +%2824%2F4%29%2At%5B1%5D+-+%2815%2F4%29%2At%5B1%5D+=+9+
(4) +24t%5B1%5D+-+15t%5B1%5D+=+36+
(4) +9t%5B1%5D+=+36+
(4) +t%5B1%5D+=+4+ hrs
and
(3) +t%5B2%5D+=+%283%2F4%29%2At%5B1%5D+
(3) +t%5B2%5D+=+%283%2F4%29%2A4+
(3) +t%5B2%5D+=+3+ hrs
--------------------------
(1 ) +24+=+x%2At%5B1%5D+
(1 ) +24+=+x%2A4+
(1 ) +x+=+6+ km/hr
and
(2) +40+=+y%2A%28+9+-+t%5B1%5D+%29+
(2) +40+=+y%2A%28+9+-+4+%29+
(2) +40+=+y%2A5+
(2) +y+=+8+ km/hr
--------------------------
check answers:
(3) +18+=+x%2At%5B2%5D+
(3) +18+=+x%2A3+
(3) +x+=+6+
and
(4) +48+=+y%2A%28+9+-+t%5B2%5D+%29+
(4) +48+=+y%2A%28+9+-+3+%29+
(4) +48+=+y%2A6+
(4) +y+=+8+
OK