SOLUTION: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express
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Question 550389: an express train makes a run of 240 km at acertain speed. Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance. find the speed of the express train in km/hr.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = speed of express train
= speed of slower train
Let = time for express train to cover km
------------
Express train:
(1)
Slower train:
(2)
-------------------------
(2)
Substitute (1) into (2)
(2)
(2)
(2)
Substitute this into (1)
(1)
(1)
(1)
(1)
Complete the square
(1)
(1)
(1)
(1)
(1)
(1)
The speed of the express train is 60 km/hr
check answer:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2) hrs
OK
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
n express train makes a run of 240 km at acertain speed.
Another train whose speed is 12 km/hr less takes an hour longer to cover the same distance.
find the speed of the express train in km/hr.
:
let s = speed of the express
then
(s-12) = speed of the other train
:
Write a time equation, time = dist/speed
:
Other train time - Express train time = 1 hr
- = 1
Multiply by s(s-12)
s(s-12)* - s(s-12)* = s(s-12)
Cancel the denominators and you have
240s - 240(s-12) = s^2 - 12s
:
240s - 240s + 2880 = s^2 - 12s
combine like terms and arrange as a quadratic equation
0 = s^2 - 12s - 2880
you can use the quadratic equation but this will factor to
(s+48)(s-60) = 0
s = 60 km/hr is the the express train
:
:
check this by finding the times of each
240/48 = 5 hrs
240/60 = 4 hrs
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