Two Towns (chpt.3)

Algebra Level 2

A group of construction workers are building a new tunnel in order to prevent traffic jams from Arrowfront to Boulderfort during the summer.

They scheduled some days for the work. It will take them 6 6 more days to build the tunnel if they pave 120 120 meters per day. In contrast, if they pave 160 160 meters per day, the tunnel will be completed 4 4 days in advance.

How long is the tunnel (in meters)?

Revisit Part 1?

Revisit Part 2?


The answer is 4800.

Ethan Mandelez by Ethan Mandelez , 15, Malaysia

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2 solutions

LCM(120,160) = 480

So it takes 4 days to reach 480 m with 120m/day and 3 days with 160m/day. Since it's finished 10 days earlier if you do 160 m a day, so the tunnel is 10x480=4800 m.

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Ethan Mandelez
May 9, 2020

This is an excess and shortage problem. In order to find the length of the tunnel, we first need to find the number of days scheduled for the work.

Shortage = 120 x 6 = 720m

Excess = 160 x 4 = 640m

We can use the equation to find out how many days which are scheduled for the work. Since

(Excess + Shortage) / Difference = Num.of Units ,

---> (720 + 640) / (160 - 120)

---> 1360 / 40 = 34 days.

We can just substitute the value (34) in to find out how long the tunnel is.

Either 34 x 120 + 6 x 120

or 34 x 160 - 4 x 160

Therefore the answer is 4800m.

0 Helpful 0 Interesting 1 Brilliant 0 Confused

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