Question 634353: Two cars start from the same point and move towards a destination that is 250km apart. They move with the speed of 60kmph and 40kmph. At certain point of time during the race, both the cars interchange their speed such that the second car reach the destination 1 hour earlier than the first car. What is the time in secs at which they interchange their speeds?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two cars start from the same point and move towards a destination that
is 250km apart.
They move with the speed of 60kmph and 40kmph.
At certain point of time during the race, both the cars interchange their
speed such that the second car reach the destination 1 hour earlier than
the first car.
What is the time in secs at which they interchange their speeds?
:
let a = travel time when they interchanged speeds (in hrs)
let b = travel time for the 1st car to complete the trip
then
(b-1) = travel time for the 2nd car to complete the trip (Arrived 1hr earlier)
:
Write a distance equation for each car, simplify the 2nd eq:
1: 60a + 40b = 250
:
2: 40a + 60(b-1) = 250
:: 40a + 60b - 60 = 250
:: 40a + 60b = 250 +60
:: 40a + 60b = 310
:
We can further simplify these equation, divide both by 10
6a + 4b = 25
and
4a + 6b = 31
:
Multiply the 1st eq by 6, the 2nd eq by 4
36a + 24b = 150
16a + 24b = 124
-----------------subtraction eliminates b, find a
20a + 0 = 26
a = 26/20
a = 1.3 hrs, for some reason, known only to them, they want the interchange time in seconds
1.3(3600) = 4680 seconds
:
:
In order to check this out we need to find b
6(1.3) + 4b = 25
4b = 25 - 7.8
b = 17.2/4
b = 4.3 hrs travel time for the 1st car to complete the trip
Check the distance
60(1.3) + 40(4.3) = 250
:
Check the distance of the 2nd car which completed the trip in 3.3 hrs
40(1.3) + 60(3.3) = 250
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