# How many km has the car travelled?

+1 vote
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A car journey is spread over five hours.

In the first hour one third of the total distance is covered.

The next hour, the car completes one third of the remaining distance.

The following hour one quarter of the remainder is covered and in the last hour the car covers half of the remaining distance.

There is now 10 km remaining.

How many km has the car travelled?

posted Jul 30, 2015

60 km

total distance = x
travel in 1st hour= 1/3 x, remainder = x-1/3x=2/3x
travel in 2nd hour= 1/3*2/3x=2/9x, remainder = 2/3x*2/3=4/9x
travel in 3rd hour= 1/4 * 4/9x=1/9x, remainder = 4/9x*3/4=1/3x
travel in 4th hour= 1/2* 1/3x=1/6x, remainder = 1/3x*1/2=1/6x
travel in 5th hour= 10 km
since the distance covered in 4th hour is the half of the reminder after 3 hours of travel, and another half is 10 km, we have 1/6x=10 ==> x=60 km

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