SOLUTION: a man cover 15 km in 3 hours, partly by walking and partly by cycling. If he walks 3km/h and cycle at 9km/h then what distance did he cycle?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: a man cover 15 km in 3 hours, partly by walking and partly by cycling. If he walks 3km/h and cycle at 9km/h then what distance did he cycle?      Log On


   

Question 697082: a man cover 15 km in 3 hours, partly by walking and partly by cycling. If he walks 3km/h and cycle at 9km/h then what distance did he cycle?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance he walked in km
+15+-+d+ = distance he cycled in km
Let +t+ = the time spent walking in hrs
+3+-+t+ = time spent cycling in hrs
--------------------------
(1) +d+=+3t+
(2) +15+-+d+=+9%2A%28+3-t+%29+
----------------------
(2) +15+-+d+=+27+-+9t+
Substitute (1) into (2)
(2) +15+-+3t+=+27+-+9t+
(2) +6t+=+27+-+15+
(2) +6t+=+12+
(2) +t+=+2+
and, since
(1) +d+=+3t+
(1) +d+=+3%2A2+
(1) +d+=+6+
+15+-+d+=+15+-+6+
+15+-+d+=+9+
He cycled 9 km
check answer:
(2) +15+-+d+=+9%2A%28+3-t+%29+
(2) +15+-+6+=+9%2A%28+3-2+%29+
(2) +9+=+9+
and
(1) +d+=+3t+
(1) +6+=+3%2A2+
(1) +6+=+6+
OK