SOLUTION: A train normally travels 60 miles at a certain speed. One day, due to bad weather, the train's speed is reduced by 10 mph so that the journey takes 3 hours longer. Find the normal
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Question 246310: A train normally travels 60 miles at a certain speed. One day, due to bad weather, the train's speed is reduced by 10 mph so that the journey takes 3 hours longer. Find the normal speed.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A train normally travels 60 miles at a certain speed. One day, due to bad weather, the train's speed is reduced by 10 mph so that the journey takes 3 hours longer.
Find the normal speed.
:
Let s = the normal speed
then
(s-10) = the slower speed
:
Write a time equation, Time = dist/speed
:
Normal time + 3 hr = Slower time
+ 3 =
:
Multiply by s(s-10), results
60(s-10) + 3s(s-10) = 60s
:
60s - 600 + 3s^2 - 30s - 60s = 0
:
Combine as a quadratic equation
3s^2 - 30s - 600 = 0
:
Simplify, divide by 3
s^2 - 10s - 200 = 0
:
Factor
(s-20)(s+10) = 0
:
Positive solution;
s = 20 mph is the normal speed
:
:
Check solution, find the times of each trip
60/10 = 6 hr, slow time
60/20 = 3 hr, normal time
-------------
diff = 3 hrs
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