SOLUTION: 1. A ship leaves a harbor sailing at 28 mph. A plane leaves 6-1/2 hours later. At what rate must it fly to overtake the ship in an hour and 15 min.? 2. A man flew to another ci

Question 1060571: 1. A ship leaves a harbor sailing at 28 mph. A plane leaves 6-1/2 hours later. At what rate must it fly to overtake the ship in an hour and 15 min.?
2. A man flew to another city for a meeting at a rate of 260 mph. He returned by train at a rate of
60 mph. If his total travel time was 4 hours, what was his flying time?
I am a home school mom trying to help my daughter with these 2 problems. I would appreciate any help. Thank you very much! Tara
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
These problems are in the category of
" related rate " problems. For word problems,
it's very important to identify their category.
-----------------------------------------
(1)
What is the head start in miles for the ship?

mi
------------------------
Let = the distance in miles the plane
travels until it catches up with the ship
-----------------------------------------
Let = the flying speed of the plane so
that the plane catches up with the ship in
hrs
-----------------------------------------
Equation for the plane:
(1)
Equation for the ship:
(2)
-----------------------------
Substitute (1) into (2)
(2)
(2)
(2)
(2)
The plane's flying rate is 173.6 mi/hr
-------------------------------------
check the answer:
(1)
(1)
(1)
and
(2)
(2)
(2)
OK
---------------------------------------
---------------------------------------
(2)
Let = his flying time in hrs
= his time traveling by train
Let = the distance to the city
------------------------------------
Equation for traveling by train:
(1)
Equation for flying:
(2)
-------------------------
substitute (2) into (1)
(1)
(1)
(1)
(1) hrs
His flying time is 3/4 of an hour, or 45 minutes
--------------------------
check the answer
(2)
(2)
(2) mi
and
(1)
(1)
(1)
(1) mi
OK
Hope this helps

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