Mathematics
Grade6
Easy

Question

Nadia scored 12 touchdowns in her first 6 minutes. ___________ touchdowns can be made by her in 20 minutes at the same rate.

  1. 60        
  2. 90
  3. 40
  4. 70

Hint:

We are given the number of touchdowns Nadia scores in 6 minutes. It’s 12 touchdowns. We have to find the number of touchdowns she will score in 20 minutes, given the rate is constant. To solve this question, we will find the rate first. We will find the rate using the first data. And from the rate we will find the required value.

The correct answer is: 40


    The given value of touchdowns is 12 and time required for 12 touchdowns is 6 minutes.
    Let’s denote the number of touchdowns by N.
    N = 12
    Time = 6 minutes
    We have to find the number of touchdowns in 20 minutes. For that, we will find the ratio of number of touchdowns to time. We will get the rate by taking the ratio. As rate is constant, we will use it to find the required value.
    Let’s find the rate.
    .        R a t e equals fraction numerator N over denominator T i m e end fraction
space space space space space space space space equals fraction numerator 12 space t o u c h d o w n s over denominator 6 space m i n u t e s end fraction
space space space space space space space space equals 2 space t o u c h d o w n s space p e r space m i n u t e                
     Now let’s use the rate to find number of touchdowns in 20 minutes
    R a t e equals fraction numerator N over denominator T i m e end fraction
    Let’s rearrange the equation for N. We will multiply both the sides by N.
    Rate × Time = N
    N = Rate × Time
    = 2 × 20
    = 40 touchdowns
    Therefore, Nadia scores 40 touchdowns in 20 minutes.

    The other method is to take the ratios and directly equate them. As the rate is constant, so the ratios will be constant. So we will consider the quantity we have to find as x and then equate the ratios. It will be a shortcut.

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