SOLUTION: if a man walks for 20 minutes and then drives in his car for an hour and a half he goes a total distance of 46 miles. If he walks for 40 minutes and then drives for one hour and t

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Question 697595: if a man walks for 20 minutes and then drives in his car for an hour and a half he goes a total distance of 46 miles. If he walks for 40 minutes and then drives for one hour and ten minutes, the speeds of walking and driving being the same as before, he travels 37 miles. Find his rates of walking and driving.
Found 2 solutions by checkley79, josmiceli:
Answer by checkley79(3341) About Me  (Show Source):
You can put this solution on YOUR website!
D=RT OR TR=D
1/3X+1.5Y=46 MULTIPLY BY -2 & ADD
2/3X+1.17Y=37
-2/3X-3Y=-92
-----------------
1.83Y=-55
Y=-55/-1.83
Y=30 MILES DRIVING.
1/3X+1.5*30=46
X/3+45=46
X/3=46-45
X/3=1
X=3
1/3*3=1 MILE WALKING.
PROOF:
2*1/3+1.17*30=37
2*3/3+35=37
6/3+35=37
2+35=37
37=37

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = his speed walking
Let +d+ = his speed driving
given:
(1) +w%2A%2820%2F60%29+%2B+d%2A90%2F60+=+46+ miles
(2) +w%2A%2840%2F60%29+%2B+d%2A%28+70%2F60%29+=+37+ miles
------------
(1) +20w+%2B+90d+=+2760+
(1) +2w+%2B+9d+=+276+
and
(2) +40w+%2B+70d+=+2220+
(2) +4w+%2B+7d+=+222+
---------------------
Multiply both sides of (1) by +2+
and subtract (2) from (1)
(1) +4w+%2B+18d+=+552+
(2) +-4w+-+7d+=+-222+
+11d+=+330+
+d+=+30+
and, since
(1) +2w+%2B+9d+=+276+
(1) +2w+%2B+270+=+276+
(1) +2w+=+6+
(1) +w+=+3+
He walks 3 mi/hr and
drives 30 mi/hr