myrddin55@gmail.com 0 Posted April 27, 2019 Report Share Posted April 27, 2019 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? Quote Link to post Share on other sites

0 rocdocmac 9 Posted April 28, 2019 Report Share Posted April 28, 2019 (edited) 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 Edited April 28, 2019 by rocdocmac Quote Link to post Share on other sites

0 Lol 0 Posted April 28, 2019 Report Share Posted April 28, 2019 133 1/3 miles Quote Link to post Share on other sites

0 Thalia 64 Posted April 30, 2019 Report Share Posted April 30, 2019 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. Quote Link to post Share on other sites

0 RuthPo 0 Posted April 30, 2019 Report Share Posted April 30, 2019 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? 1^{st} hour = 2/5 of journey = 0.4 = 8 miles 2^{nd} hour = (1/3) x (3/5) = 0.2 = 4 miles 3^{rd} hour = (1/4) of 0.2 = 0.05 = 1 mile 4^{th} hour = (0.005) = ½ mile = 0.655 20/5 = 4 miles 13.5 miles Quote Link to post Share on other sites

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## myrddin55@gmail.com 0

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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