the total time taken to travel x km at 30kph and y km at 60k

the total time taken to travel x km at 30kph and y km at 60kph is 2 1/2 hours. the time taken to travel x km at 15kph and y km at 45kph is 4hours and 20minutes. find x and y.

Solution

Rate * Time = Distance.
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in your first case you have x = 30 * 2.5 = 75 kilometers
in your second case you have y = 60 * 2.5 = 150 kilometers
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in your third case you have x = 15 * 4.33333333... = 65 kilometers
in your fourth case you have y = 45 * 4.33333333... = 195 kilometers
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these are 2 separate situations not related to each other.
you can\'t have x = 30*2.5 = 75 and x = 15 * 4.333333333... = 65 kilometers.
x is either one or the other.
if you allow x = 75 and x = 65, this would mean that 75 = 65 which is clearly false.
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if we separate the two situations, then we can conclude:
situation 1:
double the speed for the same amount of time then you get double the distance.
situation 2:
if you triple the speed for the same amount of tinme then you get triple the distance.
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outside of that i can\'t see anything else in this problem.
check the problem again and see if this is what you really wanted to know.