SOLUTION: A truck headed east 2 hours before a bus headed east from the same location. The rate of the bus was 60 mph, and the rate of the truck was 40 mph. How long did it take the bus to g

Algebra ->  Sequences-and-series -> SOLUTION: A truck headed east 2 hours before a bus headed east from the same location. The rate of the bus was 60 mph, and the rate of the truck was 40 mph. How long did it take the bus to g      Log On


   

Question 625519: A truck headed east 2 hours before a bus headed east from the same location. The rate of the bus was 60 mph, and the rate of the truck was 40 mph. How long did it take the bus to get 20 miles ahead of the truck?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The truck has a head start of
+d%5B1%5D+=+40%2A2+
+d%5B1%5D+=+80+ mi
Start a stopwatch when the bus leaves
First I'll find out when the bus catches up
with the truck
-------------
Equation for the bus:
(1) +d%5B2%5D+=+60t+
Equation for the truck:
(2) +d%5B2%5D+-+80+=+40t+
-----------------
(2) +d%5B2%5D+=+40t+%2B+80+
Substitute (1) into (2)
(2) +60t+=+40t+%2B+80+
(2) +20t+=+80+
(2) +t+=+4+ hrs
and
(1) +d%5B2%5D+=+60t+
(1) +d%5B2%5D+=+60%2A4+
(1) +d%5B2%5D+=+240+ mi
-----------------
Now the truck continues on for distance =
+d%5B3%5D+ mi
During this time the bus must travel
+d%5B3%5D+%2B+20+ mi
---------------
Equation for bus:
(1) +d%5B3%5D+%2B+20+=+60t+
Equation for truck:
(2) +d%5B3%5D+=+40t+
---------------
substitute (2) into (1)
(1) +40t+%2B+20+=+60t+
(1) +20t+=+20+
(1) +t+=+1+ hr
-------------
The elapsed time on the stop watch is
+4+%2B+1+=+5+
The bus gets 20 mi ahead of the truck in 5 hrs
------------
check answer:
The total distance for the bus is
+d%5B2%5D+%2B+d%5B3%5D+%2B+20+=+240+%2B+40+%2B+20+
+d%5B2%5D+%2B+d%5B3%5D+%2B+20+=+300+ mi
The total distance for the truck is
+d%5B2%5D+-+80+%2B+d%5B3%5D+=+80+%2B+240+-+80+%2B+40+
+d%5B2%5D+-+80+%2B+d%5B3%5D+=+280+
Equation for bus:
+300+=+60t+
+t+=+5+ hrs
Equation for truck:
+200+=+40t+
+t+=+5+ hrs
OK