Nia and Joseph are making fruit bowls. Joseph cuts the fruit, and Nia distribute

Question

Nia and Joseph are making fruit bowls. Joseph cuts the fruit, and Nia distributes the fruit into the bowls. Joseph cuts 4 pieces of fruit per minute and Nia distributes 10 pieces of fruit per minute. Josph had already cut 72 pieces of fruit when Nia started. Joseph continues to cut fruit at the same rate. How many minutes will it take for Nia to catch up to Joseph.

Here is a similar problem:

Nia and Joseph are making fruit bowls. Joseph cuts the fruit, and Nia distributes the fruit into the bowls. Joseph cuts 3 pieces of fruit per minute and Nia distributes 9 pieces of fruit per minute.

Josph had already cut 72 pieces of fruit when Nia started. Joseph continues to cut fruit at the same rate. How many minutes will it take for Nia to catch up to Joseph.

Defining the variable:

Suppose it takes Nia t minutes to catch up.

In t minutes Nia will distribute 9t pieces of fruit,

by then Joseph will have cut a total of (72+3t) pieces of fruit.

Setting up the equation:

9t = 72+3t

Solving the equation:

9t = 72+3t

Þ 9t -3t = 72

Þ 6t = 72

Þ t = 72/6 = 12

Ans: It will take Nia 12 minutes to catch up.

Explanation / Answer

Suppose it takes t minutes to catch up.

so, In t minutes Nia will distribute = 9t pieces

Joseph cut a total = (72+3t) pieces

so, setting the equations, we have:

9t = 72 + 3t

Solving :

9t = 72 + 3t

=> 9t - 3t = 72

=> 6t = 72

=> t = 72/6

=> t = 12

Hence, 12 minutes will it take for Nia to catch up to Joseph.

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