# algebra

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a car goes at a constant speed for 120 kms, on the way back he goes at half the speed. he drives for a total of 4 hours and 30 minutes. what are the two speeds?

• algebra -

let the speed on the first trip be x km/h
then the speed on the return trip will be x/2 km/h

Time for first part = 120/x hours
and on the return trip = 120/(x/2) = 240/x hours

then 120/x + 240/x = 4.5
360/x = 4.5
x = 360/4.5
= 80

so he went 80 km/h for the first part and only 40 km/h on the way back.

check:
time for first part = 120/80 = 1.5 hrs
on way back = 120/40 = 3 hrs, for a total of 4.5 hrs.

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