SOLUTION: A truck left a depot at noon traveling an average of 40 kilometers per hour. How far from the depot and at what time will it overtake another truck, which left the same depot 2 hou

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Question 668771: A truck left a depot at noon traveling an average of 40 kilometers per hour. How far from the depot and at what time will it overtake another truck, which left the same depot 2 hours earlier and was traveling 30 kilometers per hour?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The truck that left earlier had a head start of
+30%2A2+=+60+ km
Let +d+ = distance the truck that left at noon went
until it overtook the earlier truck
Let +t+ = time to overtake earlier truck
Equation for truck that left at noon:
(1) +d+=+40t+
Equation for truck that left 2 hrs earlier:
(2) +d+-+60+=+30t+
------------------
(2) +d+=+60+%2B+30t+
By substitution:
+40t+=+60+%2B+30t+
+10t+=+60+
+t+=+6+
At 6 PM the 2nd truck overtakes the 1st
+d+=+40t+
+d+=+40%2A6+
+d+=+240+
the 2nd truck overtakes the 1st 240 km from depot
check:
(2) +d+-+60+=+30t+
(2) +d+-+60+=+30%2A6+
(2) +d+=+60+%2B+180+
(2) +d+=+240+ km
OK