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help with this question would be appreciated

A family have been stuck in bank holiday traffic for the last four hours.

In the first hour they covered two fifths of their total journey.

The next hour they covered one third of what was left.

The following hour they covered one quarter of the remainder, 

and in the fourth hour half of the remaining distance.

The family still have 20 miles left to travel.

How many miles have they travelled so far?

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Spoiler

1st hr: travel = 2/5 (0.4); distance left = 1 - 2/5  = 3/5 (0.6)

2nd hr: travel = 1/3 * 3/5 = 3/15 = 1/5 (0.2); left = 3/5 - 1/5 = 2/5 (0.4)

3rd hr: travel = 1/4 * 2/5 = 2/20 (0.1); left = 2/5 - 2/20 = 4/10 - 1/10 = 3/10 ( 0.3)

4th hr: travel = 1/2 * 3/10 = 3/20 (0.15); left = 3/10 - 3/20 = 6/20 - 3/20 = 3/20  (0.15)

Remaining distance to travel = 0.15 = 20 miles

Total distance traveled = 100 - 0.15 = 0.85 = 20 * 0.85/0.15 = 113⅓ miles

image.png.3f553e215afd4e4f1367c94c41553318.png

 

Edited by rocdocmac

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A visual approach.

You can represent the whole trip as a rectangle (or circle or other shape) and divide it into 5ths. Shade in sections as you go. You'll have to do a little more dividing for the 3rd and 4th hours but those numbers work out pretty well.

Hour 1: 3/5 left (2 of 5 sections gone)

Hour 2: 2/5 left (1 of 3 sections gone)

Hour 3: split the 2 remaining sections in half so you have 4 sections, each 1/10 of the total. 3/10 left (1 of 4 sections gone)

Hour 4: split in half again giving 6 sections, each 1/20 of the whole. 3/20 left (1 of 6 sections gone). 

(3/20)x = 20 miles

Solve for x.

This obviously wouldn't work well with numbers that aren't so nice but I learn better with pictures. 

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A family have been stuck in bank holiday traffic for the last four hours. In the first hour they covered two fifths of their total journey. The next hour they covered one third of what was left. The following hour they covered one quarter of the remainder,  and in the fourth hour half of the remaining distance. The family still have 20 miles left to travel. How many miles have they travelled so far?

 

1st hour = 2/5 of journey = 0.4 = 8 miles

2nd hour = (1/3) x (3/5) = 0.2 = 4 miles

3rd hour = (1/4) of 0.2 = 0.05 = 1 mile

4th hour = (0.005) = ½ mile

= 0.655

20/5 = 4 miles

13.5 miles

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