Question

susan take thrice as much time as alex to bake a cake. if the work together they can finish the cake in 9 hours in how many hours Susan bake the cake alone ?
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Answer 1

Given,

3× Baking time of Alex = Baking time of Susan

Together they can bake the cake in 9 hours.

To find,

The time that Susan will take to bake the cake alone.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Let, the baking time of Alex = x hours

(Assume, x as a variable to do the further mathematical calculations.)

Baking time of Susan = 3×x = 3x hours

And, let the whole work = 1

For Alex,

x hours for = 1

1 hour for = 1/x

For Susan,

3x hours for = 1

1 hour for = 1/3x

So, together in 1 hour they can do = (1/x + 1/3x) = (3+1)/3x = 4/3x work

They do,

4/3x work in = 1 hour

1 work in = 3x/4 hours

According to the data mentioned in the question,

3x/4 = 9

3x = 36

x = 12

Susan's baking time = 3x = 3×12 = 36 hours

Hence, Susan alone can bake the cake in 36 hours.