A roofer requires 15 hours to shingle a roof, while an apprentice requires 21 hours. Write
an equation that can be used to find the time in hours, t, it would take to shingle the roof if
both worked together. Solve the equation.

The equation in terms of "t"

1/t = ¹/₂₁ + ¹/₁₅

On solving the equation "t"= 8 ³/₄ days

Step-by-step explanation:

Time taken by roofer to shingle a roof- 15 hours

Time taken by apprentice-21 hours

Time required to shingle if both worked together- “t” hours

If roofer shingles the roof in 15 hours

Part of the roof he would shingle in 1 hours= ¹/₁₅

Similarly, part of the roof shingled by apprentice in 1 hour- ¹/₂₁

Part of the roof shingles when they worked together for 1 hours-                    1/t = ¹/₂₁ + ¹/₁₅

Total time taken= 1/t = ¹/₂₁ + ¹/₁₅

1/t= ⁽²¹⁺¹⁵⁾ /₃₁₅

t= 315/36 = 8 ³/₄ days

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.