James can bake 2 muffins in 7 minutes. Alex can bake 4 muffins in 15 minutes. James starts baking muffins at 1.30 p.m and Kylie joins him at 1.45 p.m. If both of them work straight through at the above rates, at what time will they finish baking the 54th muffin ?

The correct option is C 3 : 15 p.m

Step 1 : Underline key words
James can bake 2 muffins in 7 minutes. Kylie can bake 4 muffins in 15 minutes. James starts baking muffins at 1.30 p.m and Kylie joins him at 1.45 p.m. If both of them work straight through at the above rates, at what time will they finish baking the 54th muffin?

Step 2 :
Define the variables : Let 'j' represent the number of minutes James spend baking the muffins and 'k' be the number of minutes Kylie spend baking the muffins.

Decipher the relation b/w the variables :
Total muffins baked = Rate at which the muffins are baked $\times$ Time taken
James bakes 2 muffins in 7 minutes. Therefore, total number of muffins baked by James in 'j' minutes $=\left(\frac{2}{7}\right)j$
Kylie bakes 4 muffins in 15 minutes. Therefore, total number of muffins baked by Kylie in 'k' minutes $=\left(\frac{4}{15}\right)k$
Since, we want to know when they will bake a total of 54 muffins. Therefore,
$\left(\frac{2}{7}\right)j+\left(\frac{4}{15}\right)k=54$
We also know, James work 15 minutes more than Kylie. Therefore,
j = k +15
Solving the two equation using substitution method.
$\left(\frac{2}{7}\right)(k+15)+\left(\frac{4}{15}\right)k=54$
$\left(\frac{2}{7}\right)k+\frac{30}{7}+\left(\frac{4}{15}\right)k=54$
$\left(\frac{2}{7}\right)k+\left(\frac{4}{15}\right)k+\frac{30}{7}=54$
$\left(\frac{58}{105}\right)k=54-\frac{30}{7}$
$K=90$
Putting the value in the equation j= k + 15, we get
J = 105
We want to know when is the 54th muffin baked. We now know, James starts baking from 1.30 p.m and bakes for 105 minutes or 1 hour 45 minutes.
So, they finish baking 54 muffins at 3.15 p.m
We Know, Kylie started working at 1.45 p.m and works for 90 minutes or 1 hour and 30 minutes. Thus, they finish baking at 3.15 p.m
Either way, they finish baking at 3.15 p.m

Hence, option C is correct.