SOLUTION: Mr. Bean tries to push his car up an 800m slope to a petrol station. In one hour he pushes the car 200m up the hill. The next hour he rests and slips back 100m. How long does it ta

Question 1025431: Mr. Bean tries to push his car up an 800m slope to a petrol station. In one hour he pushes the car 200m up the hill. The next hour he rests and slips back 100m. How long does it take to reach the top of the hill if he keeps pushing and resting in this way.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
he moves the car forward 200 meters and then slides back 100 meters every 2 hours.

in the last 2 hours, he moves the car forward 200 meters and doesn't have to rest because he's made it to the top of the hill and his ordeal is over.

so for 600 meters he makes an average progress of 100 meters every 2 hours which is equal to 50 meters every hour.

in the last hour he makes 200 meters.

the total number of hours is therefore equal to 600 / 50 + 1 = 13 hours.

in the 13 hours, if x is the hour, then:

if the hour is odd he makes 200 miles.
if the hour is even he loses 100 miles.

there are 7 odd numbered hours and 6 even numbered hours.

the odd numbered hours are 1,3,5,7,9,11,13
the even numbered hours are 2,4,6,8,10,12

the total number of miles progressed is therefore 7 * 200 - 6 * 100 which is equal to 1400 - 600 = 800.

the solution checks out and the number of hours required is 13.

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