SOLUTION: A ship leaves a harbour travelling at 25 km/h ,15 minutes later another ship leaves travelling at 28 km/h. How long will it take the second ship to catch up to the first? Please,pl

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: A ship leaves a harbour travelling at 25 km/h ,15 minutes later another ship leaves travelling at 28 km/h. How long will it take the second ship to catch up to the first? Please,pl      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 878621: A ship leaves a harbour travelling at 25 km/h ,15 minutes later another ship leaves travelling at 28 km/h. How long will it take the second ship to catch up to the first? Please,please help I worked it out and got 2 hours and 25 minutes but I don't know if it is right.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
How much of a head start does the 1st ship have?
+15+ min = +1%2F4+ hr
+d%5B1%5D+=+25%2A%281%2F4%29+
+d%5B1%5D+=+6.25+ km
-------------------
Start a stopwatch when the 2nd ship leaves
Let +t+ = the time in hrs on the stopwatch when
the 2nd ship catches the 1st ship
Let +d+ = the distance the 2nd ship travels
until it catches the 1st ship
------------------------
Equation for the 1st ship:
(1) +d+-+6.25+=+25t+
Equation for the 2nd ship:
(2) +d+=+28t+
----------------
Substitute (2) into (1)
(1) +28t+-+6.25+=+25t+
(1) +3t+=+6.25+
(1) +t+=+2.08333+
Convert +.08333+ hrs to min
+.08333%2A60+=+5+ min
The 2nd ship will catches the 1st
in 2 hrs 5 min
-------------------
check:
(2) +d+=+28t+
(2) +d+=+28%2A2.08333+
(2) +d+=+58.333+ km
and
(1) +d+-+6.25+=+25t+
(1) +d+-+6.25+=+25%2A2.08333+
(1) +d+=+58.333+ km
OK