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Time taken by Bruce and Bryce to complete the work is $1hour20minutes.$

Time taken by Marty and Bryce to complete the work is $1hourand36minutes$

Time taken by Bruce and Marty to complete the work is $2hoursand40minutes$

Let the time taken for Bruce, Bryce and Marty be denoted by $x,y,z$respectively.

Convert the time in hours to minutes,

$1$hour $20$minutes$=60+20$

role="math" localid="1647004053693" $=80$minutes

$1$hour $36$ minutes $=60+36$

role="math" localid="1647004099456" $=96$minutes

$2$hour $40$ minutes $=120+40$

$=160$ minutes.

The system of linear equation from the given information is formatted as:

$\left\{\begin{array}{l}\frac{1}{x}+\frac{1}{y}=\frac{1}{80}\\ \frac{1}{y}+\frac{1}{z}=\frac{1}{96}\\ \frac{1}{x}+\frac{1}{z}=\frac{1}{160}\end{array}\right.$

Subtract second equation from first equation,

$$\begin{gathered} \frac{1}{x}-\frac{1}{z}=\frac{1}{80}-\frac{1}{96} \\ \frac{1}{x}-\frac{1}{z}=\frac{16}{7680} \\ \frac{1}{x}-\frac{1}{z}=\frac{1}{480} \end{gathered}$$

Add above equation with the third equation, we get,

$$\begin{gathered} \frac{1}{x}-\frac{1}{z}+\frac{1}{x}+\frac{1}{z}=\frac{1}{480}+\frac{1}{160} \\ \frac{2}{x}=\frac{640}{76800} \\ \frac{2}{x}=\frac{1}{120} \\ \frac{1}{x}=\frac{1}{240} \end{gathered}$$

Substitute $x=240$in the first equation,

$$\begin{gathered} \frac{1}{240}+\frac{1}{y}=\frac{1}{80} \\ \frac{1}{y}=\frac{1}{80}-\frac{1}{240} \\ =\frac{2}{240} \\ =\frac{1}{120} \end{gathered}$$

Substitute $y=120$in second equation,

$$\begin{gathered} \frac{1}{y}+\frac{1}{z}=\frac{1}{160} \\ \frac{1}{120}+\frac{1}{z}=\frac{1}{160} \\ \frac{1}{z}=\frac{1}{160}-\frac{1}{120} \\ =\frac{1}{480} \end{gathered}$$

$x=240$ minutes

$$\begin{gathered} =\frac{240}{60} \\ =4hours \end{gathered}$$

$y=120minutes$

$$\begin{gathered} =\frac{120}{60} \\ =2hours \end{gathered}$$

$z=480minutes$

$$\begin{gathered} =\frac{480}{60} \\ =8hours \end{gathered}$$